diff --git a/Project.toml b/Project.toml
index 43e23dc1..4388fa0c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -10,7 +10,7 @@ MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
 GLPK = "1"
 Ipopt = "1"
 JuMP = "1"
-MathOptInterface = "1.3"
+MathOptInterface = "1.13.2"
 SCS = "1"
 julia = "1.6"
 
diff --git a/README.md b/README.md
index b45da9b0..9c51660d 100644
--- a/README.md
+++ b/README.md
@@ -37,7 +37,7 @@ using JuMP, HiGHS
 import ParametricOptInterface as POI
 model = Model(() -> POI.Optimizer(HiGHS.Optimizer()))
 @variable(model, x)
-@variable(model, p in POI.Parameter(1.0))
+@variable(model, p in MOI.Parameter(1.0))
 @constraint(model, cons, x + p >= 3)
 @objective(model, Min, 2x)
 optimize!(model)
diff --git a/benchmark/MOI_benchmarks.jl b/benchmark/MOI_benchmarks.jl
index 60386540..c9a1e8a6 100644
--- a/benchmark/MOI_benchmarks.jl
+++ b/benchmark/MOI_benchmarks.jl
@@ -117,7 +117,7 @@ function generate_poi_problem(model, data::PMedianData, add_parameters::Bool)
     if add_parameters
         d, cd = MOI.add_constrained_variable(
             model,
-            POI.Parameter(data.num_facilities),
+            MOI.Parameter(data.num_facilities),
         )
     end
 
diff --git a/benchmark/run_benchmarks.jl b/benchmark/run_benchmarks.jl
index 3ca572a2..fd4b2943 100644
--- a/benchmark/run_benchmarks.jl
+++ b/benchmark/run_benchmarks.jl
@@ -24,14 +24,14 @@ end
 
 function poi_add_parameters(N::Int)
     model = POI.Optimizer(MOI.Utilities.Model{Float64}())
-    MOI.add_constrained_variable.(model, POI.Parameter.(ones(N)))
+    MOI.add_constrained_variable.(model, MOI.Parameter.(ones(N)))
     return nothing
 end
 
 function poi_add_parameters_and_variables(N::Int)
     model = POI.Optimizer(MOI.Utilities.Model{Float64}())
     MOI.add_variables(model, N / 2)
-    MOI.add_constrained_variable.(model, POI.Parameter.(ones(Int(N / 2))))
+    MOI.add_constrained_variable.(model, MOI.Parameter.(ones(Int(N / 2))))
     return nothing
 end
 
@@ -39,7 +39,7 @@ function poi_add_parameters_and_variables_alternating(N::Int)
     model = POI.Optimizer(MOI.Utilities.Model{Float64}())
     for i in 1:Int(N / 2)
         MOI.add_variable(model)
-        MOI.add_constrained_variable(model, POI.Parameter(1))
+        MOI.add_constrained_variable(model, MOI.Parameter(1.0))
     end
     return nothing
 end
@@ -77,7 +77,7 @@ function poi_add_saf_variables_and_parameters_ctr(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -103,7 +103,7 @@ function poi_add_saf_variables_and_parameters_ctr_parameter_update(
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -162,7 +162,7 @@ function poi_add_sqf_variables_parameters_ctr(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -186,7 +186,7 @@ function poi_add_sqf_variables_parameters_ctr_parameter_update(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -212,7 +212,7 @@ function poi_add_sqf_parameters_parameters_ctr(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -236,7 +236,7 @@ function poi_add_sqf_parameters_parameters_ctr_parameter_update(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -288,7 +288,7 @@ function poi_add_saf_variables_and_parameters_obj(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -314,7 +314,7 @@ function poi_add_saf_variables_and_parameters_obj_parameter_update(
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -375,7 +375,7 @@ function poi_add_sqf_variables_parameters_obj(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -399,7 +399,7 @@ function poi_add_sqf_variables_parameters_obj_parameter_update(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -427,7 +427,7 @@ function poi_add_sqf_parameters_parameters_obj(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
@@ -451,7 +451,7 @@ function poi_add_sqf_parameters_parameters_obj_parameter_update(N::Int, M::Int)
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             )
         )
     for _ in 1:M
diff --git a/benchmark/run_benchmarks_jump.jl b/benchmark/run_benchmarks_jump.jl
index 9ddc49e9..fe95b743 100644
--- a/benchmark/run_benchmarks_jump.jl
+++ b/benchmark/run_benchmarks_jump.jl
@@ -43,7 +43,7 @@ function poi_add_parameters(N::Int)
             ),
         ),
     )
-    @variable(model, x[i = 1:N] in POI.Parameter(1))
+    @variable(model, x[i = 1:N] in MOI.Parameter(1.0))
     return nothing
 end
 
@@ -56,7 +56,7 @@ function poi_add_parameters_and_variables(N::Int)
             ),
         ),
     )
-    @variable(model, x[i = 1:N] in POI.Parameter(1))
+    @variable(model, x[i = 1:N] in MOI.Parameter(1.0))
     return nothing
 end
 
@@ -71,7 +71,7 @@ function poi_add_parameters_and_variables_alternating(N::Int)
     )
     for i in 1:Int(N / 2)
         @variable(model)
-        @variable(model, set = POI.Parameter(1))
+        @variable(model, set = MOI.Parameter(1.0))
     end
     return nothing
 end
@@ -112,7 +112,7 @@ function poi_add_saf_variables_and_parameters_ctr(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(0))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(0))
     @constraint(model, con[i = 1:M], sum(x) + sum(p) >= 1)
     return nothing
 end
@@ -130,7 +130,7 @@ function poi_add_saf_variables_and_parameters_ctr_parameter_update(
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(0))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(0))
     @constraint(model, con[i = 1:M], sum(x) + sum(p) >= 1)
     MOI.set.(model, POI.ParameterValue(), p, 0.5)
     POI.update_parameters!(backend(model))
@@ -173,7 +173,7 @@ function poi_add_sqf_variables_parameters_ctr(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     @constraint(model, con[i = 1:M], dot(x, p) >= 1)
     return nothing
 end
@@ -188,7 +188,7 @@ function poi_add_sqf_variables_parameters_ctr_parameter_update(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     @constraint(model, con[i = 1:M], dot(x, p) >= 1)
     MOI.set.(model, POI.ParameterValue(), p, 0.5)
     POI.update_parameters!(backend(model))
@@ -205,7 +205,7 @@ function poi_add_sqf_parameters_parameters_ctr(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     @constraint(model, con[i = 1:M], dot(p, p) >= 1)
     return nothing
 end
@@ -220,7 +220,7 @@ function poi_add_sqf_parameters_parameters_ctr_parameter_update(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     @constraint(model, con[i = 1:M], dot(p, p) >= 1)
     MOI.set.(model, POI.ParameterValue(), p, 0.5)
     POI.update_parameters!(backend(model))
@@ -265,7 +265,7 @@ function poi_add_saf_variables_and_parameters_obj(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     for _ in 1:M
         @objective(model, Min, sum(x) + sum(p))
     end
@@ -285,7 +285,7 @@ function poi_add_saf_variables_and_parameters_obj_parameter_update(
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     for _ in 1:M
         @objective(model, Min, sum(x) + sum(p))
     end
@@ -336,7 +336,7 @@ function poi_add_sqf_variables_parameters_obj(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     for _ in 1:M
         @objective(model, Min, dot(x, p))
     end
@@ -353,7 +353,7 @@ function poi_add_sqf_variables_parameters_obj_parameter_update(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     for _ in 1:M
         @objective(model, Min, dot(x, p))
     end
@@ -374,7 +374,7 @@ function poi_add_sqf_parameters_parameters_obj(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     for _ in 1:M
         @objective(model, Min, dot(p, p))
     end
@@ -391,7 +391,7 @@ function poi_add_sqf_parameters_parameters_obj_parameter_update(N::Int, M::Int)
         ),
     )
     @variable(model, x[i = 1:Int(N / 2)])
-    @variable(model, p[i = 1:Int(N / 2)] in POI.Parameter.(1))
+    @variable(model, p[i = 1:Int(N / 2)] in MOI.Parameter.(1))
     for _ in 1:M
         @objective(model, Min, dot(p, p))
     end
diff --git a/benchmark/run_benders_quantile_regression_benchmark.jl b/benchmark/run_benders_quantile_regression_benchmark.jl
index fcebb0c5..7765efec 100644
--- a/benchmark/run_benders_quantile_regression_benchmark.jl
+++ b/benchmark/run_benders_quantile_regression_benchmark.jl
@@ -142,7 +142,7 @@ function slave_model(PARAM, K)
         @variable(slave, β[i = 1:N_Candidates] == 0, Param())
     elseif PARAM == 1
         # Create parameters
-        @variable(slave, β[i = 1:N_Candidates] in POI.Parameter.(0))
+        @variable(slave, β[i = 1:N_Candidates] in MOI.Parameter.(0.0))
     else
         # Create fixed variables
         @variables(slave, begin
diff --git a/docs/src/Examples/benders.md b/docs/src/Examples/benders.md
index 5b707214..2fb10ace 100644
--- a/docs/src/Examples/benders.md
+++ b/docs/src/Examples/benders.md
@@ -153,7 +153,7 @@ function inner_model(K)
 
     # create the regression coefficient representation
     # Create parameters
-    β = [@variable(inner, set = POI.Parameter(0)) for i in 1:N_Candidates]
+    β = [@variable(inner, set = MOI.Parameter(0.0)) for i in 1:N_Candidates]
     for (i, βi) in enumerate(β)
         set_name(βi, "β[$i]")
     end
diff --git a/docs/src/Examples/example.md b/docs/src/Examples/example.md
index 0d9fc4df..cdad6370 100644
--- a/docs/src/Examples/example.md
+++ b/docs/src/Examples/example.md
@@ -26,12 +26,12 @@ for x_i in x
 end
 ```
 
-Now, let's consider 3 [`ParametricOptInterface.Parameter`](@ref). Two of them, `y`, `z`, will be placed in the constraints and one, `w`, in the objective function. We'll start all three of them with a value equal to `0`:
+Now, let's consider 3 `MOI.Parameter`. Two of them, `y`, `z`, will be placed in the constraints and one, `w`, in the objective function. We'll start all three of them with a value equal to `0`:
 
 ```@example moi1
-w, cw = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-z, cz = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+w, cw = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+z, cz = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
 ```
 
 Let's add the constraints. Notice that we treat parameters and variables in the same way when building the functions that will be placed in some set to create a constraint (`Function-in-Set`):
@@ -146,12 +146,12 @@ We declare the variable `x` as in a typical `JuMP` model:
 @variable(model, x[i = 1:2] >= 0)
 ```
 
-Now, let's consider 3 [`ParametricOptInterface.Parameter`](@ref). Two of them, `y`, `z`, will be placed in the constraints and one, `w`, in the objective function. We'll start all three of them with a value equal to `0`:
+Now, let's consider 3 `MOI.Parameter`. Two of them, `y`, `z`, will be placed in the constraints and one, `w`, in the objective function. We'll start all three of them with a value equal to `0`:
 
 ```@example jump1
-@variable(model, y in ParametricOptInterface.Parameter(0))
-@variable(model, z in ParametricOptInterface.Parameter(0))
-@variable(model, w in ParametricOptInterface.Parameter(0))
+@variable(model, y in MOI.Parameter(0.0))
+@variable(model, z in MOI.Parameter(0.0))
+@variable(model, w in MOI.Parameter(0.0))
 ```
 
 Let's add the constraints. Notice that we treat parameters the same way we treat variables when writing the model:
@@ -246,9 +246,9 @@ const POI = ParametricOptInterface
 
 model = Model(() -> ParametricOptInterface.Optimizer(HiGHS.Optimizer()))
 @variable(model, x[i = 1:3] >= 0)
-@variable(model, p1[i = 1:3] in ParametricOptInterface.Parameter(0))
-@variable(model, p2[i = 1:3] in ParametricOptInterface.Parameter.([1, 10, 45]))
-@variable(model, p3[i = 1:3] in ParametricOptInterface.Parameter.(ones(3)))
+@variable(model, p1[i = 1:3] in MOI.Parameter(0.0))
+@variable(model, p2[i = 1:3] in MOI.Parameter.([1, 10, 45]))
+@variable(model, p3[i = 1:3] in MOI.Parameter.(ones(3)))
 ```
 
 ## JuMP Example - Dealing with parametric expressions as variable bounds
@@ -263,11 +263,11 @@ const POI = ParametricOptInterface
 
 model = direct_model(POI.Optimizer(HiGHS.Optimizer()))
 @variable(model, x)
-@variable(model, p in POI.Parameter(0.0))
+@variable(model, p in MOI.Parameter(0.0))
 @constraint(model, x >= p)
 ```
 
-Since parameters are treated like variables JuMP lowers this to MathOptInterface as `x - p >= 0` which is not a variable bound but a linear constraint.This means that the current representation of this problem at the solver level is:
+Since parameters are treated like variables JuMP lowers this to MOI as `x - p >= 0` which is not a variable bound but a linear constraint.This means that the current representation of this problem at the solver level is:
 
 ```math
 \begin{align}
@@ -288,7 +288,7 @@ const POI = ParametricOptInterface
 
 model = direct_model(POI.Optimizer(HiGHS.Optimizer()))
 @variable(model, x)
-@variable(model, p in POI.Parameter(0.0))
+@variable(model, p in MOI.Parameter(0.0))
 
 # Indicate that all the new constraints will be valid variable bounds
 MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_BOUNDS)
@@ -343,7 +343,7 @@ MOI.set(optimizer, MOI.ObjectiveSense(), MOI.MAX_SENSE)
 obj_func = MOI.ScalarQuadraticFunction(
     [MOI.ScalarQuadraticTerm(1.0, x, x)
     MOI.ScalarQuadraticTerm(1.0, y, y)],
-    MathOptInterface.ScalarAffineTerm{Float64}[],
+    MOI.ScalarAffineTerm{Float64}[],
     0.0,
 )
 MOI.set(
@@ -357,7 +357,7 @@ To multiply a parameter in a quadratic term, the user will
 need to use the `POI.QuadraticObjectiveCoef` model attribute.
 
 ```@example moi2
-p = first(MOI.add_constrained_variable.(optimizer, POI.Parameter(1.0)))
+p = first(MOI.add_constrained_variable.(optimizer, MOI.Parameter(1.0)))
 MOI.set(optimizer, POI.QuadraticObjectiveCoef(), (x,y), p)
 ```
 
@@ -403,7 +403,7 @@ model = direct_model(optimizer)
 
 @variable(model, x >= 0)
 @variable(model, y >= 0)
-@variable(model, p in POI.Parameter(1.0))
+@variable(model, p in MOI.Parameter(1.0))
 @constraint(model, 2x + y <= 4)
 @constraint(model, x + 2y <= 4)
 @objective(model, Max, (x^2 + y^2)/2)
@@ -447,7 +447,7 @@ POI currently works with NLPs when users wish to add the parameters to the non-N
 ```julia
 @variable(model, x)
 @variable(model, y)
-@variable(model, z in POI.Parameter(10))
+@variable(model, z in MOI.Parameter(10))
 @constraint(model, x + y >= z)
 @NLobjective(model, Min, x^2 + y^2)
 ```
@@ -457,7 +457,7 @@ but does not work with models that have parameters on the NL expressions like th
 ```julia
 @variable(model, x)
 @variable(model, y)
-@variable(model, z in POI.Parameter(10))
+@variable(model, z in MOI.Parameter(10))
 @constraint(model, x + y >= z)
 @NLobjective(model, Min, x^2 + y^2 + z) # There is a parameter here
 ```
@@ -481,7 +481,7 @@ POI_cached_optimizer() = POI.Optimizer(cached())
 model = Model(() -> POI_cached_optimizer())
 @variable(model, x)
 @variable(model, y)
-@variable(model, z in POI.Parameter(10))
+@variable(model, z in MOI.Parameter(10))
 @constraint(model, x + y >= z)
 @NLobjective(model, Min, x^2 + y^2)
 ```
@@ -493,7 +493,7 @@ If users wish to make modifications on variable bounds the POI interface will he
 ```julia
 model = Model(() -> POI.Optimizer(Ipopt.Optimizer()))
 @variable(model, x)
-@variable(model, z in POI.Parameter(10))
+@variable(model, z in MOI.Parameter(10))
 MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_BOUNDS)
 @constraint(model, x >= z)
 @NLobjective(model, Min, x^2)
diff --git a/docs/src/Examples/markowitz.md b/docs/src/Examples/markowitz.md
index 73d4fcd0..800fd595 100644
--- a/docs/src/Examples/markowitz.md
+++ b/docs/src/Examples/markowitz.md
@@ -47,7 +47,7 @@ function first_model(μ,Σ)
     
     N = length(μ)
     @variable(portfolio, x[1:N] >= 0)
-    @variable(portfolio, γ in POI.Parameter(0.0))
+    @variable(portfolio, γ in MOI.Parameter(0.0))
 
     @objective(portfolio, Max, γ*dot(μ,x) - x' * Σ * x)
     @constraint(portfolio, sum(x) == 1)
diff --git a/docs/src/manual.md b/docs/src/manual.md
index 696aff6d..d8ff2e1e 100644
--- a/docs/src/manual.md
+++ b/docs/src/manual.md
@@ -56,22 +56,26 @@ optimizer = POI.Optimizer(HiGHS.Optimizer())
 
 ### Parameters
 
-A [`ParametricOptInterface.Parameter`](@ref) is a variable with a fixed value that can be changed by the user.
+A `MOI.Parameter` is a set used to define a variable with a fixed value that
+can be changed by the user. It is analogous to `MOI.EqualTo`, but can be used
+by special methods like the ones in this package to remove the fixed variable from the
+optimization problem. This permits the usage of multiplicative parameters in lienar models
+and might speedup solves since the number of variables is reduced.
 
 ### Adding a new parameter to a model
 
-To add a parameter to a model, we must use the `MOI.add_constrained_variable()` function, passing as its arguments the model and a [`ParametricOptInterface.Parameter`](@ref) with its given value:
+To add a parameter to a model, we must use the `MOI.add_constrained_variable()` function, passing as its arguments the model and a `MOI.Parameter` with its given value:
 
 ```julia
-y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
 ```
 
 ### Changing the parameter value
 
-To change a given parameter's value, access its `VariableIndex` and set it to the new value using the [`ParametricOptInterface.Parameter`](@ref) structure.
+To change a given parameter's value, access its `VariableIndex` and set it to the new value using the `MOI.Parameter` structure.
 
 ```julia
-MOI.set(optimizer, POI.ParameterValue(), y, POI.Parameter(2.0))
+MOI.set(optimizer, POI.ParameterValue(), y, MOI.Parameter(2.0))
 ```
 
 ### Retrieving the dual of a parameter
diff --git a/docs/src/reference.md b/docs/src/reference.md
index a978374a..acb5eba3 100644
--- a/docs/src/reference.md
+++ b/docs/src/reference.md
@@ -3,7 +3,6 @@
 ```@docs
 ParametricOptInterface.ConstraintsInterpretation
 ParametricOptInterface.Optimizer
-ParametricOptInterface.Parameter
 ParametricOptInterface.ParameterDual
 ParametricOptInterface.ParameterValue
 ```
\ No newline at end of file
diff --git a/src/ParametricOptInterface.jl b/src/ParametricOptInterface.jl
index e0ab8fc1..cf0aacf5 100644
--- a/src/ParametricOptInterface.jl
+++ b/src/ParametricOptInterface.jl
@@ -16,23 +16,6 @@ const PARAMETER_INDEX_THRESHOLD = Int64(4_611_686_018_427_387_904) # div(typemax
 const SIMPLE_SCALAR_SETS{T} =
     Union{MOI.LessThan{T},MOI.GreaterThan{T},MOI.EqualTo{T}}
 
-"""
-    Parameter(val::Float64)
-
-The `Parameter` structure stores the numerical value associated to a given
-parameter.
-
-## Example
-
-```julia-repl
-julia> ParametricOptInterface.Parameter(5)
-ParametricOptInterface.Parameter(5)
-```
-"""
-struct Parameter <: MOI.AbstractScalarSet
-    val::Float64
-end
-
 # Utilities for using a CleverDict in Parameters
 struct ParameterIndex
     index::Int64
@@ -161,6 +144,9 @@ mutable struct Optimizer{T,OT<:MOI.ModelLike} <: MOI.AbstractOptimizer
     last_variable_index_added::Int64
     last_parameter_index_added::Int64
 
+    # mapping of all constraints: necessary for getters
+    constraint_outer_to_inner::DoubleDict{MOI.ConstraintIndex}
+
     # affine constraint data
     last_affine_added::Int64
     # Store the map for SAFs (some might be transformed into VI)
@@ -234,6 +220,7 @@ mutable struct Optimizer{T,OT<:MOI.ModelLike} <: MOI.AbstractOptimizer
             ),
             0,
             PARAMETER_INDEX_THRESHOLD,
+            DoubleDict{MOI.ConstraintIndex}(),
             # affine constraint
             0,
             DoubleDict{MOI.ConstraintIndex}(),
@@ -280,6 +267,7 @@ function MOI.is_empty(model::Optimizer)
            isempty(model.variables) &&
            model.last_variable_index_added == 0 &&
            model.last_parameter_index_added == PARAMETER_INDEX_THRESHOLD &&
+           isempty(model.constraint_outer_to_inner) &&
            # affine ctr
            model.last_affine_added == 0 &&
            isempty(model.affine_outer_to_inner) &&
@@ -311,6 +299,7 @@ function MOI.empty!(model::Optimizer{T}) where {T}
     empty!(model.variables)
     model.last_variable_index_added = 0
     model.last_parameter_index_added = PARAMETER_INDEX_THRESHOLD
+    empty!(model.constraint_outer_to_inner)
     # affine ctr
     model.last_affine_added = 0
     empty!(model.affine_outer_to_inner)
@@ -636,6 +625,17 @@ function MOI.get(
         return MOI.get(model.optimizer, attr, ci)
     end
 end
+function MOI.get(
+    model::Optimizer{T},
+    ::MOI.ConstraintFunction,
+    cp::MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{T}},
+) where {T}
+    p = MOI.VariableIndex(cp.value)
+    if !is_parameter_in_model(model, p)
+        error("Parameter not in the model")
+    end
+    return p
+end
 
 function MOI.get(
     model::Optimizer,
@@ -702,10 +702,6 @@ function MOI.set(model::Optimizer, attr::MOI.AbstractOptimizerAttribute, value)
     return
 end
 
-function MOI.get(model::Optimizer, ::MOI.NumberOfConstraints{F,S}) where {F,S}
-    return length(MOI.get(model, MOI.ListOfConstraintIndices{F,S}()))
-end
-
 function MOI.get(
     model::Optimizer,
     attr::MOI.ConstraintSet,
@@ -739,83 +735,30 @@ function MOI.get(model::Optimizer, attr::MOI.ResultCount)
     return MOI.get(model.optimizer, attr)
 end
 
-# TODO: cleanup
-# In the AbstractBridgeOptimizer, we collect all the possible constraint types and them filter with NumberOfConstraints.
-# If NumberOfConstraints is zero then we remove it from the list.
-# Here, you can look over keys(quadratic_outer_to_inner) and add the F-S types of all the keys in constraints.
-# To implement NumberOfConstraints, you call NumberOfConstraints to the inner optimizer.
-# Then you remove the number of constraints of that that in values(quadratic_outer_to_inner)
 function MOI.get(model::Optimizer, ::MOI.ListOfConstraintTypesPresent)
-    inner_ctrs = MOI.get(model.optimizer, MOI.ListOfConstraintTypesPresent())
-    if !has_quadratic_constraint_caches(model)
-        return inner_ctrs
-    end
-
-    cache_keys = collect(keys(model.quadratic_outer_to_inner))
-    constraints = Set{Tuple{DataType,DataType}}()
-
-    for (F, S) in inner_ctrs
-        inner_index =
-            MOI.get(model.optimizer, MOI.ListOfConstraintIndices{F,S}())
-        cache_map_check =
-            quadratic_constraint_cache_map_check.(model, inner_index)
-        for type in typeof.(cache_keys[cache_map_check])
-            push!(constraints, (type.parameters[1], type.parameters[2]))
-        end
-        # If not all the constraints are cached then also push the original type
-        # since there was a function with no parameters of that type
-        if !all(cache_map_check)
-            push!(constraints, (F, S))
-        end
-    end
-
-    return collect(constraints)
-end
-
-function MOI.get(
-    model::Optimizer,
-    attr::MOI.ListOfConstraintIndices{F,S},
-) where {S,F<:Union{MOI.VectorOfVariables,MOI.VariableIndex}}
-    return MOI.get(model.optimizer, attr)
+    constraint_types = MOI.Utilities.DoubleDicts.nonempty_outer_keys(
+        model.constraint_outer_to_inner,
+    )
+    return collect(constraint_types)
 end
 
 function MOI.get(
     model::Optimizer,
     ::MOI.ListOfConstraintIndices{F,S},
-) where {
-    S<:MOI.AbstractSet,
-    F<:Union{MOI.ScalarAffineFunction{T},MOI.VectorAffineFunction{T}},
-} where {T}
-    inner_index = MOI.get(model.optimizer, MOI.ListOfConstraintIndices{F,S}())
-    if !has_quadratic_constraint_caches(model)
-        return inner_index
-    end
-
-    cache_map_check = quadratic_constraint_cache_map_check(mode, inner_index)
-    return inner_index[cache_map_check]
+) where {S,F}
+    list = collect(values(model.constraint_outer_to_inner[F, S]))
+    sort!(list, lt = (x, y) -> (x.value < y.value))
+    return list
 end
 
-function MOI.get(
-    model::Optimizer,
-    ::MOI.ListOfConstraintIndices{F,S},
-) where {S<:MOI.AbstractSet,F<:MOI.ScalarQuadraticFunction{T}} where {T}
-    inner_index = MOI.ConstraintIndex{F,S}[]
-    if MOI.supports_constraint(model.optimizer, F, S)
-        inner_index =
-            MOI.get(model.optimizer, MOI.ListOfConstraintIndices{F,S}())
-    end
-    if !has_quadratic_constraint_caches(model)
-        return inner_index
-    end
-
-    for key in keys(model.quadratic_outer_to_inner)
-        push!(inner_index, key)
-    end
-
-    return inner_index
+function MOI.get(model::Optimizer, ::MOI.NumberOfConstraints{F,S}) where {S,F}
+    return length(model.constraint_outer_to_inner[F, S])
 end
 
-function MOI.supports_add_constrained_variable(::Optimizer, ::Type{Parameter})
+function MOI.supports_add_constrained_variable(
+    ::Optimizer{T},
+    ::Type{MOI.Parameter{T}},
+) where {T}
     return true
 end
 
@@ -834,18 +777,36 @@ function MOI.add_variable(model::Optimizer)
     )
 end
 
-function MOI.add_constrained_variable(model::Optimizer, set::Parameter)
+function MOI.add_constrained_variable(
+    model::Optimizer{T},
+    set::MOI.Parameter{T},
+) where {T}
     next_parameter_index!(model)
     p = MOI.VariableIndex(model.last_parameter_index_added)
-    MOI.Utilities.CleverDicts.add_item(model.parameters, set.val)
-    cp = MOI.ConstraintIndex{MOI.VariableIndex,Parameter}(
+    MOI.Utilities.CleverDicts.add_item(model.parameters, set.value)
+    cp = MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{T}}(
         model.last_parameter_index_added,
     )
+    _add_to_constraint_map!(model, cp)
     MOI.Utilities.CleverDicts.add_item(model.updated_parameters, NaN)
     update_number_of_parameters!(model)
     return p, cp
 end
 
+function _add_to_constraint_map!(model::Optimizer, ci)
+    model.constraint_outer_to_inner[ci] = ci
+    return
+end
+function _add_to_constraint_map!(model::Optimizer, ci_in, ci_out)
+    model.constraint_outer_to_inner[ci_out] = ci_in
+    return
+end
+function _add_constraint_direct_and_cache_map!(model::Optimizer, f, set)
+    ci = MOI.add_constraint(model.optimizer, f, set)
+    _add_to_constraint_map!(model, ci)
+    return ci
+end
+
 function MOI.add_constraint(
     model::Optimizer,
     f::MOI.VariableIndex,
@@ -856,7 +817,7 @@ function MOI.add_constraint(
     elseif !is_variable_in_model(model, f)
         error("Variable not in the model")
     end
-    return MOI.add_constraint(model.optimizer, f, set)
+    return _add_constraint_direct_and_cache_map!(model, f, set)
 end
 
 function add_constraint_with_parameters_on_function(
@@ -902,7 +863,7 @@ function add_saf_constraint(
         model.last_affine_added,
     )
     model.affine_outer_to_inner[outer_ci] = inner_ci
-    # model.outer_to_inner_map[outer_ci] = inner_ci
+    model.constraint_outer_to_inner[outer_ci] = inner_ci
     model.affine_constraint_cache[inner_ci] = pf
     model.affine_constraint_cache_set[inner_ci] = set
     return outer_ci
@@ -924,7 +885,7 @@ function add_vi_constraint(
         model.last_affine_added,
     )
     model.affine_outer_to_inner[outer_ci] = inner_ci
-    # model.outer_to_inner_map[outer_ci] = inner_ci
+    model.constraint_outer_to_inner[outer_ci] = inner_ci
     model.affine_constraint_cache[inner_ci] = pf
     model.affine_constraint_cache_set[inner_ci] = set
     return outer_ci
@@ -936,7 +897,7 @@ function MOI.add_constraint(
     set::MOI.AbstractScalarSet,
 ) where {T}
     if !function_has_parameters(f)
-        return MOI.add_constraint(model.optimizer, f, set)
+        return _add_constraint_direct_and_cache_map!(model, f, set)
     else
         return add_constraint_with_parameters_on_function(model, f, set)
     end
@@ -990,16 +951,32 @@ function MOI.get(
 end
 
 function MOI.set(
-    model::Optimizer,
+    model::Optimizer{T},
     ::MOI.ConstraintSet,
-    cp::MOI.ConstraintIndex{MOI.VariableIndex,Parameter},
-    set::Parameter,
-)
+    cp::MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{T}},
+    set::MOI.Parameter{T},
+) where {T}
     p = MOI.VariableIndex(cp.value)
     if !is_parameter_in_model(model, p)
         error("Parameter not in the model")
     end
-    return model.updated_parameters[p_idx(p)] = set.val
+    return model.updated_parameters[p_idx(p)] = set.value
+end
+
+function MOI.get(
+    model::Optimizer{T},
+    ::MOI.ConstraintSet,
+    cp::MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{T}},
+) where {T}
+    p = MOI.VariableIndex(cp.value)
+    if !is_parameter_in_model(model, p)
+        error("Parameter not in the model")
+    end
+    val = model.updated_parameters[p_idx(p)]
+    if isnan(val)
+        return MOI.Parameter{T}(model.parameters[p_idx(p)])
+    end
+    return MOI.Parameter{T}(val)
 end
 
 """
@@ -1026,8 +1003,9 @@ function MOI.set(
     var::MOI.VariableIndex,
     val::Float64,
 )
-    ci = MOI.ConstraintIndex{MOI.VariableIndex,Parameter}(var.value)
-    set = MOI.set(opt, MOI.ConstraintSet(), ci, Parameter(val))
+    ci =
+        MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{Float64}}(var.value)
+    set = MOI.set(opt, MOI.ConstraintSet(), ci, MOI.Parameter(val))
     return nothing
 end
 
@@ -1037,8 +1015,9 @@ function MOI.set(
     var::MOI.VariableIndex,
     val::Float64,
 )
-    ci = MOI.ConstraintIndex{MOI.VariableIndex,Parameter}(var.value)
-    set = MOI.set(model, MOI.ConstraintSet(), ci, Parameter(val))
+    ci =
+        MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{Float64}}(var.value)
+    set = MOI.set(model, MOI.ConstraintSet(), ci, MOI.Parameter(val))
     return nothing
 end
 
@@ -1065,9 +1044,10 @@ function MOI.get(
     ::ParameterValue,
     var::MOI.VariableIndex,
 )
-    ci = MOI.ConstraintIndex{MOI.VariableIndex,Parameter}(var.value)
+    ci =
+        MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{Float64}}(var.value)
     set = MOI.get(opt, MOI.ConstraintSet(), ci)
-    return set.val
+    return set.value
 end
 
 function MOI.get(model::Optimizer, ::ParameterValue, var::MOI.VariableIndex)
@@ -1256,7 +1236,7 @@ function MOI.add_constraint(
     if function_has_parameters(f)
         error("VectorOfVariables does not allow parameters")
     end
-    return MOI.add_constraint(model.optimizer, f, set)
+    return _add_constraint_direct_and_cache_map!(model, f, set)
 end
 
 function MOI.add_constraint(
@@ -1265,7 +1245,7 @@ function MOI.add_constraint(
     set::MOI.AbstractVectorSet,
 ) where {T}
     if !function_has_parameters(f)
-        return MOI.add_constraint(model.optimizer, f, set)
+        return _add_constraint_direct_and_cache_map!(model, f, set)
     else
         return add_constraint_with_parameters_on_function(model, f, set)
     end
@@ -1281,6 +1261,7 @@ function add_constraint_with_parameters_on_function(
     update_cache!(pf, model)
     inner_ci = MOI.add_constraint(model.optimizer, current_function(pf), set)
     model.vector_affine_constraint_cache[inner_ci] = pf
+    _add_to_constraint_map!(model, inner_ci)
     return inner_ci
 end
 
@@ -1307,7 +1288,7 @@ function add_constraint_with_parameters_on_function(
             model.last_quad_add_added,
         )
         model.quadratic_outer_to_inner[outer_ci] = inner_ci
-        # model.outer_to_inner_map[outer_ci] = inner_ci
+        model.constraint_outer_to_inner[outer_ci] = inner_ci
     else
         fa = MOI.ScalarAffineFunction(func.affine_terms, func.constant)
         inner_ci = MOI.Utilities.normalize_and_add_constraint(
@@ -1322,7 +1303,7 @@ function add_constraint_with_parameters_on_function(
         # This part is used to remember that ci came from a quadratic function
         # It is particularly useful because sometimes the constraint mutates
         model.quadratic_outer_to_inner[outer_ci] = inner_ci
-        # model.outer_to_inner_map[outer_ci] = inner_ci
+        model.constraint_outer_to_inner[outer_ci] = inner_ci
     end
     model.quadratic_constraint_cache[inner_ci] = pf
     model.quadratic_constraint_cache_set[inner_ci] = s
@@ -1335,7 +1316,7 @@ function MOI.add_constraint(
     set::MOI.AbstractScalarSet,
 ) where {T}
     if !function_has_parameters(f)
-        return MOI.add_constraint(model.optimizer, f, set)
+        return _add_constraint_direct_and_cache_map!(model, f, set)
     else
         return add_constraint_with_parameters_on_function(model, f, set)
     end
@@ -1345,6 +1326,54 @@ function MOI.delete(model::Optimizer, v::MOI.VariableIndex)
     delete!(model.variables, v)
     MOI.delete(model.optimizer, v)
     MOI.delete(model.original_objective_cache, v)
+    # TODO - what happens if the variable was in a SAF that was converted to bounds?
+    # solution: do not allow if that is the case (requires going trhought the scalar affine cache)
+    # TODO - deleting a variable also deletes constraints
+    for (F, S) in MOI.Utilities.DoubleDicts.nonempty_outer_keys(
+        model.constraint_outer_to_inner,
+    )
+        _delete_variable_index_constraint(
+            model.constraint_outer_to_inner,
+            F,
+            S,
+            v.value,
+        )
+    end
+    return
+end
+
+function _delete_variable_index_constraint(d, F, S, v)
+    return
+end
+function _delete_variable_index_constraint(
+    d,
+    F::Type{MOI.VariableIndex},
+    S,
+    value,
+)
+    inner = d[F, S]
+    for k in keys(inner)
+        if k.value == value
+            delete!(inner, k)
+        end
+    end
+    return
+end
+
+function MOI.delete(
+    model::Optimizer,
+    c::MOI.ConstraintIndex{F,S},
+) where {F<:MOI.ScalarQuadraticFunction,S<:MOI.AbstractSet}
+    if haskey(model.quadratic_outer_to_inner, c)
+        ci_inner = model.quadratic_outer_to_inner[c]
+        deleteat!(model.quadratic_outer_to_inner, c)
+        deleteat!(model.quadratic_constraint_cache, c)
+        deleteat!(model.quadratic_constraint_cache_set, c)
+        MOI.delete(model.optimizer, ci_inner)
+    else
+        MOI.delete(model.optimizer, c)
+    end
+    deleteat!(model.constraint_outer_to_inner, c)
     return
 end
 
@@ -1352,10 +1381,16 @@ function MOI.delete(
     model::Optimizer,
     c::MOI.ConstraintIndex{F,S},
 ) where {F<:MOI.ScalarAffineFunction,S<:MOI.AbstractSet}
-    if haskey(model.affine_constraint_cache, c)
+    if haskey(model.affine_outer_to_inner, c)
+        ci_inner = model.affine_outer_to_inner[c]
+        delete!(model.affine_outer_to_inner, c)
         delete!(model.affine_constraint_cache, c)
+        delete!(model.affine_constraint_cache_set, c)
+        MOI.delete(model.optimizer, ci_inner)
+    else
+        MOI.delete(model.optimizer, c)
     end
-    MOI.delete(model.optimizer, c)
+    delete!(model.constraint_outer_to_inner, c)
     return
 end
 
@@ -1364,6 +1399,7 @@ function MOI.delete(
     c::MOI.ConstraintIndex{F,S},
 ) where {F<:Union{MOI.VariableIndex,MOI.VectorOfVariables},S<:MOI.AbstractSet}
     MOI.delete(model.optimizer, c)
+    delete!(model.constraint_outer_to_inner, c)
     return
 end
 
@@ -1372,6 +1408,7 @@ function MOI.delete(
     c::MOI.ConstraintIndex{F,S},
 ) where {F<:MOI.VectorAffineFunction,S<:MOI.AbstractSet}
     MOI.delete(model.optimizer, c)
+    delete!(model.constraint_outer_to_inner, c)
     deleteat!(model.vector_affine_constraint_cache, c)
     return
 end
@@ -1533,13 +1570,14 @@ function _poi_default_copy_to(dest::T, src::MOI.ModelLike) where {T}
             Any[
                 MOI.get(src, MOI.ListOfConstraintIndices{F,S}()) for
                 (F, S) in MOI.get(src, MOI.ListOfConstraintTypesPresent()) if
-                MOI.Utilities._is_variable_function(F) && S != Parameter
+                MOI.Utilities._is_variable_function(F) &&
+                    S != MOI.Parameter{Float64}
             ],
             Any[MOI.Utilities._try_constrain_variables_on_creation(
                 dest,
                 src,
                 index_map,
-                Parameter,
+                MOI.Parameter{Float64},
             )],
         )
     else
diff --git a/src/duals.jl b/src/duals.jl
index 7c2140b1..0a74646f 100644
--- a/src/duals.jl
+++ b/src/duals.jl
@@ -107,10 +107,14 @@ struct ParameterDual <: MOI.AbstractVariableAttribute end
 
 MOI.is_set_by_optimize(::ParametricOptInterface.ParameterDual) = true
 
-function MOI.get(model::Optimizer, ::ParameterDual, v::MOI.VariableIndex)
+function MOI.get(
+    model::Optimizer{T},
+    ::ParameterDual,
+    v::MOI.VariableIndex,
+) where {T}
     if !is_additive(
         model,
-        MOI.ConstraintIndex{MOI.VariableIndex,Parameter}(v.value),
+        MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{T}}(v.value),
     )
         error("Cannot compute the dual of a multiplicative parameter")
     end
@@ -118,10 +122,10 @@ function MOI.get(model::Optimizer, ::ParameterDual, v::MOI.VariableIndex)
 end
 
 function MOI.get(
-    model::Optimizer,
+    model::Optimizer{T},
     ::MOI.ConstraintDual,
-    cp::MOI.ConstraintIndex{MOI.VariableIndex,Parameter},
-)
+    cp::MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{T}},
+) where {T}
     if !is_additive(model, cp)
         error("Cannot compute the dual of a multiplicative parameter")
     end
diff --git a/test/jump_tests.jl b/test/jump_tests.jl
index b99a1696..2dd27999 100644
--- a/test/jump_tests.jl
+++ b/test/jump_tests.jl
@@ -7,9 +7,9 @@ function test_jump_direct_affine_parameters()
     optimizer = POI.Optimizer(GLPK.Optimizer())
     model = direct_model(optimizer)
     @variable(model, x[i = 1:2] >= 0)
-    @variable(model, y in POI.Parameter(0))
-    @variable(model, w in POI.Parameter(0))
-    @variable(model, z in POI.Parameter(0))
+    @variable(model, y in MOI.Parameter(0.0))
+    @variable(model, w in MOI.Parameter(0.0))
+    @variable(model, z in MOI.Parameter(0.0))
     @constraint(model, 2 * x[1] + x[2] + y <= 4)
     @constraint(model, 1 * x[1] + 2 * x[2] + z <= 4)
     @objective(model, Max, 4 * x[1] + 3 * x[2] + w)
@@ -30,9 +30,9 @@ function test_jump_direct_parameter_times_variable()
     optimizer = POI.Optimizer(GLPK.Optimizer())
     model = direct_model(optimizer)
     @variable(model, x[i = 1:2] >= 0)
-    @variable(model, y in POI.Parameter(0))
-    @variable(model, w in POI.Parameter(0))
-    @variable(model, z in POI.Parameter(0))
+    @variable(model, y in MOI.Parameter(0.0))
+    @variable(model, w in MOI.Parameter(0.0))
+    @variable(model, z in MOI.Parameter(0.0))
     @constraint(model, 2 * x[1] + x[2] + y <= 4)
     @constraint(model, (1 + y) * x[1] + 2 * x[2] + z <= 4)
     @objective(model, Max, 4 * x[1] + 3 * x[2] + w)
@@ -52,9 +52,9 @@ end
 function test_jump_affine_parameters()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
     @variable(model, x[i = 1:2] >= 0)
-    @variable(model, y in POI.Parameter(0))
-    @variable(model, w in POI.Parameter(0))
-    @variable(model, z in POI.Parameter(0))
+    @variable(model, y in MOI.Parameter(0.0))
+    @variable(model, w in MOI.Parameter(0.0))
+    @variable(model, z in MOI.Parameter(0.0))
     @constraint(model, 2 * x[1] + x[2] + y <= 4)
     @constraint(model, 1 * x[1] + 2 * x[2] + z <= 4)
     @objective(model, Max, 4 * x[1] + 3 * x[2] + w)
@@ -74,9 +74,9 @@ end
 function test_jump_parameter_times_variable()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
     @variable(model, x[i = 1:2] >= 0)
-    @variable(model, y in POI.Parameter(0))
-    @variable(model, w in POI.Parameter(0))
-    @variable(model, z in POI.Parameter(0))
+    @variable(model, y in MOI.Parameter(0.0))
+    @variable(model, w in MOI.Parameter(0.0))
+    @variable(model, z in MOI.Parameter(0.0))
     @test MOI.get(model, POI.ParameterValue(), y) == 0
     @constraint(model, 2 * x[1] + x[2] + y <= 4)
     @constraint(model, (1 + y) * x[1] + 2 * x[2] + z <= 4)
@@ -104,7 +104,7 @@ function test_jump_constraintfunction_getter()
         ),
     )
     vx = @variable(model, x[i = 1:2])
-    vp = @variable(model, p[i = 1:2] in POI.Parameter.(-1))
+    vp = @variable(model, p[i = 1:2] in MOI.Parameter.(-1.0))
     c1 = @constraint(model, con, sum(x) + sum(p) >= 1)
     c2 = @constraint(model, conq, sum(x .* p) >= 1)
     c3 = @constraint(model, conqa, sum(x .* p) + x[1]^2 + x[1] + p[1] >= 1)
@@ -255,19 +255,24 @@ function test_jump_interpret_parameteric_bounds()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
     MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_BOUNDS)
     @variable(model, x[i = 1:2])
-    @variable(model, p[i = 1:2] in POI.Parameter.(-1))
+    @variable(model, p[i = 1:2] in MOI.Parameter.(-1.0))
     @constraint(model, [i in 1:2], x[i] >= p[i])
     @objective(model, Min, sum(x))
     optimize!(model)
-    @test MOI.get(model, MOI.ListOfConstraintTypesPresent()) ==
-          Tuple{Type,Type}[
+    expected = Tuple{Type,Type}[
         (MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64}),
-        (MOI.VariableIndex, POI.Parameter),
+        (MOI.VariableIndex, MOI.Parameter{Float64}),
     ]
-    @test MOI.get(
+    result = MOI.get(model, MOI.ListOfConstraintTypesPresent())
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
+    expected = Tuple{Type,Type}[(MOI.VariableIndex, MOI.GreaterThan{Float64})]
+    result = MOI.get(
         backend(model).optimizer.model.optimizer,
         MOI.ListOfConstraintTypesPresent(),
-    ) == Tuple{Type,Type}[(MOI.VariableIndex, MOI.GreaterThan{Float64})]
+    )
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
     @test objective_value(model) == -2
     MOI.set(model, POI.ParameterValue(), p[1], 4.0)
     optimize!(model)
@@ -279,19 +284,24 @@ function test_jump_interpret_parameteric_bounds_expression()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
     MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_BOUNDS)
     @variable(model, x[i = 1:2])
-    @variable(model, p[i = 1:2] in POI.Parameter.(-1))
+    @variable(model, p[i = 1:2] in MOI.Parameter.(-1.0))
     @constraint(model, [i in 1:2], x[i] >= p[i] + p[1])
     @objective(model, Min, sum(x))
     optimize!(model)
-    @test MOI.get(model, MOI.ListOfConstraintTypesPresent()) ==
-          Tuple{Type,Type}[
+    expected = Tuple{Type,Type}[
         (MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64}),
-        (MOI.VariableIndex, POI.Parameter),
+        (MOI.VariableIndex, MOI.Parameter{Float64}),
     ]
-    @test MOI.get(
+    result = MOI.get(model, MOI.ListOfConstraintTypesPresent())
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
+    expected = Tuple{Type,Type}[(MOI.VariableIndex, MOI.GreaterThan{Float64})]
+    result = MOI.get(
         backend(model).optimizer.model.optimizer,
         MOI.ListOfConstraintTypesPresent(),
-    ) == Tuple{Type,Type}[(MOI.VariableIndex, MOI.GreaterThan{Float64})]
+    )
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
     @test objective_value(model) == -4
     MOI.set(model, POI.ParameterValue(), p[1], 4.0)
     optimize!(model)
@@ -303,16 +313,22 @@ function test_jump_direct_interpret_parameteric_bounds()
     model = direct_model(POI.Optimizer(GLPK.Optimizer()))
     MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_BOUNDS)
     @variable(model, x[i = 1:2])
-    @variable(model, p[i = 1:2] in POI.Parameter.(-1))
+    @variable(model, p[i = 1:2] in MOI.Parameter.(-1.0))
     @constraint(model, [i in 1:2], x[i] >= p[i])
     @objective(model, Min, sum(x))
     optimize!(model)
-    @test MOI.get(model, MOI.ListOfConstraintTypesPresent()) ==
-          Tuple{Type,Type}[(MOI.VariableIndex, MOI.GreaterThan{Float64})]
-    @test MOI.get(
-        backend(model).optimizer,
-        MOI.ListOfConstraintTypesPresent(),
-    ) == Tuple{Type,Type}[(MOI.VariableIndex, MOI.GreaterThan{Float64})]
+    expected = Tuple{Type,Type}[
+        (MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64}),
+        (MOI.VariableIndex, MOI.Parameter{Float64}),
+    ]
+    result = MOI.get(model, MOI.ListOfConstraintTypesPresent())
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
+    expected = Tuple{Type,Type}[(MOI.VariableIndex, MOI.GreaterThan{Float64})]
+    result =
+        MOI.get(backend(model).optimizer, MOI.ListOfConstraintTypesPresent())
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
     @test objective_value(model) == -2
     MOI.set(model, POI.ParameterValue(), p[1], 4.0)
     optimize!(model)
@@ -324,22 +340,25 @@ function test_jump_direct_interpret_parameteric_bounds_no_interpretation()
     model = direct_model(POI.Optimizer(GLPK.Optimizer()))
     MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_CONSTRAINTS)
     @variable(model, x[i = 1:2])
-    @variable(model, p[i = 1:2] in POI.Parameter.(-1))
+    @variable(model, p[i = 1:2] in MOI.Parameter.(-1.0))
     @constraint(model, [i in 1:2], x[i] >= p[i])
     @objective(model, Min, sum(x))
     optimize!(model)
-    @test MOI.get(model, MOI.ListOfConstraintTypesPresent()) ==
-          Tuple{Type,Type}[(
-        MOI.ScalarAffineFunction{Float64},
-        MOI.GreaterThan{Float64},
-    )]
-    @test MOI.get(
-        backend(model).optimizer,
-        MOI.ListOfConstraintTypesPresent(),
-    ) == Tuple{Type,Type}[(
+    expected = Tuple{Type,Type}[
+        (MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64}),
+        (MOI.VariableIndex, MOI.Parameter{Float64}),
+    ]
+    result = MOI.get(model, MOI.ListOfConstraintTypesPresent())
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
+    expected = Tuple{Type,Type}[(
         MOI.ScalarAffineFunction{Float64},
         MOI.GreaterThan{Float64},
-    )]
+    ),]
+    result =
+        MOI.get(backend(model).optimizer, MOI.ListOfConstraintTypesPresent())
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
     @test objective_value(model) == -2
     MOI.set(model, POI.ParameterValue(), p[1], 4.0)
     optimize!(model)
@@ -351,7 +370,7 @@ function test_jump_direct_interpret_parameteric_bounds_change()
     model = direct_model(POI.Optimizer(GLPK.Optimizer()))
     MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_BOUNDS)
     @variable(model, x[i = 1:2])
-    @variable(model, p[i = 1:2] in POI.Parameter.(-1))
+    @variable(model, p[i = 1:2] in MOI.Parameter.(-1.0))
     @constraint(model, [i in 1:2], x[i] >= p[i])
     @test_throws ErrorException @constraint(model, [i in 1:2], 2x[i] >= p[i])
     MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_CONSTRAINTS)
@@ -369,7 +388,7 @@ function test_jump_direct_interpret_parameteric_bounds_both()
     model = direct_model(POI.Optimizer(GLPK.Optimizer()))
     MOI.set(model, POI.ConstraintsInterpretation(), POI.BOUNDS_AND_CONSTRAINTS)
     @variable(model, x[i = 1:2])
-    @variable(model, p[i = 1:2] in POI.Parameter.(-1))
+    @variable(model, p[i = 1:2] in MOI.Parameter.(-1.0))
     @constraint(model, [i in 1:2], x[i] >= p[i])
     @constraint(model, [i in 1:2], 2x[i] >= p[i])
     @objective(model, Min, sum(x))
@@ -385,7 +404,7 @@ function test_jump_direct_interpret_parameteric_bounds_invalid()
     model = direct_model(POI.Optimizer(GLPK.Optimizer()))
     MOI.set(model, POI.ConstraintsInterpretation(), POI.ONLY_BOUNDS)
     @variable(model, x[i = 1:2])
-    @variable(model, p[i = 1:2] in POI.Parameter.(-1))
+    @variable(model, p[i = 1:2] in MOI.Parameter.(-1.0))
     @test_throws ErrorException @constraint(
         model,
         [i in 1:2],
@@ -405,7 +424,7 @@ function test_jump_set_variable_start_value()
     optimizer = POI.Optimizer(cached)
     model = direct_model(optimizer)
     @variable(model, x >= 0)
-    @variable(model, p in POI.Parameter(0))
+    @variable(model, p in MOI.Parameter(0.0))
     set_start_value(x, 1.0)
     @test start_value(x) == 1
     err = ErrorException(
@@ -420,7 +439,7 @@ function test_jump_direct_get_parameter_value()
     model = direct_model(POI.Optimizer(GLPK.Optimizer()))
     @variable(model, x, lower_bound = 0.0, upper_bound = 10.0)
     @variable(model, y, binary = true)
-    @variable(model, z, set = POI.Parameter(10))
+    @variable(model, z, set = MOI.Parameter(10.0))
     c = @constraint(model, 19.0 * x - z + 22.0 * y <= 1.0)
     @objective(model, Min, x + y)
     @test MOI.get(model, POI.ParameterValue(), z) == 10
@@ -431,7 +450,7 @@ function test_jump_get_parameter_value()
     model = Model(() -> ParametricOptInterface.Optimizer(GLPK.Optimizer()))
     @variable(model, x, lower_bound = 0.0, upper_bound = 10.0)
     @variable(model, y, binary = true)
-    @variable(model, z, set = POI.Parameter(10))
+    @variable(model, z, set = MOI.Parameter(10))
     c = @constraint(model, 19.0 * x - z + 22.0 * y <= 1.0)
     @objective(model, Min, x + y)
     @test MOI.get(model, POI.ParameterValue(), z) == 10
@@ -449,7 +468,7 @@ function test_jump_sdp_scalar_parameter()
     optimizer = POI.Optimizer(cached)
     m = direct_model(optimizer)
     set_silent(m)
-    @variable(m, p in POI.Parameter(0))
+    @variable(m, p in MOI.Parameter(0.0))
     @variable(m, x[1:2, 1:2], Symmetric)
     @objective(m, Min, x[1, 1] + x[2, 2])
     @constraint(m, LinearAlgebra.Symmetric(x .- [1+p 0; 0 1+p]) in PSDCone())
@@ -473,7 +492,7 @@ function test_jump_sdp_matrix_parameter()
     m = direct_model(optimizer)
     set_silent(m)
     P1 = [1 2; 2 3]
-    @variable(m, p[1:2, 1:2] in POI.Parameter.(P1))
+    @variable(m, p[1:2, 1:2] in MOI.Parameter.(P1))
     @variable(m, x[1:2, 1:2], Symmetric)
     @objective(m, Min, x[1, 1] + x[2, 2])
     @constraint(m, LinearAlgebra.Symmetric(x - p) in PSDCone())
@@ -488,7 +507,7 @@ end
 
 function test_jump_dual_basic()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, x[1:2] in POI.Parameter.(ones(2) .* 4.0))
+    @variable(model, x[1:2] in MOI.Parameter.(ones(2) .* 4.0))
     @variable(model, y[1:6])
     @constraint(model, ctr1, 3 * y[1] >= 2 - 7 * x[1])
     @objective(model, Min, 5 * y[1])
@@ -503,7 +522,7 @@ end
 function test_jump_dual_multiplicative_fail()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
     @variable(model, x)
-    @variable(model, p in POI.Parameter(1.0))
+    @variable(model, p in MOI.Parameter(1.0))
     @constraint(model, cons, x * p >= 3)
     @objective(model, Min, 2x)
     optimize!(model)
@@ -516,7 +535,7 @@ end
 function test_jump_dual_objective_min()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
     @variable(model, x)
-    @variable(model, p in POI.Parameter(1.0))
+    @variable(model, p in MOI.Parameter(1.0))
     @constraint(model, cons, x >= 3 * p)
     @objective(model, Min, 2x + p)
     optimize!(model)
@@ -527,7 +546,7 @@ end
 function test_jump_dual_objective_max()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
     @variable(model, x)
-    @variable(model, p in POI.Parameter(1.0))
+    @variable(model, p in MOI.Parameter(1.0))
     @constraint(model, cons, x >= 3 * p)
     @objective(model, Max, -2x + p)
     optimize!(model)
@@ -537,7 +556,7 @@ end
 
 function test_jump_dual_multiple_parameters_1()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, x[1:6] in POI.Parameter.(ones(6) .* 4.0))
+    @variable(model, x[1:6] in MOI.Parameter.(ones(6) .* 4.0))
     @variable(model, y[1:6])
     @constraint(model, ctr1, 3 * y[1] >= 2 - 7 * x[3])
     @constraint(model, ctr2, 3 * y[1] >= 2 - 7 * x[3])
@@ -571,7 +590,7 @@ end
 
 function test_jump_duals_LessThan()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α in POI.Parameter(-1.0))
+    @variable(model, α in MOI.Parameter(-1.0))
     @variable(model, x)
     cref = @constraint(model, x ≤ α)
     @objective(model, Max, x)
@@ -590,7 +609,7 @@ end
 
 function test_jump_duals_EqualTo()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α in POI.Parameter(-1.0))
+    @variable(model, α in MOI.Parameter(-1.0))
     @variable(model, x)
     cref = @constraint(model, x == α)
     @objective(model, Max, x)
@@ -608,7 +627,7 @@ end
 
 function test_jump_duals_GreaterThan()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α in POI.Parameter(1.0))
+    @variable(model, α in MOI.Parameter(1.0))
     MOI.set(model, POI.ParameterValue(), α, -1.0)
     @variable(model, x)
     cref = @constraint(model, x >= α)
@@ -627,7 +646,7 @@ end
 
 function test_jump_dual_multiple_parameters_2()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α[1:10] in POI.Parameter.(ones(10)))
+    @variable(model, α[1:10] in MOI.Parameter.(ones(10)))
     @variable(model, x)
     cref = @constraint(model, x == sum(2 * α[i] for i in 1:10))
     @objective(model, Min, x)
@@ -640,7 +659,7 @@ end
 
 function test_jump_dual_mixing_params_and_vars_1()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α[1:5] in POI.Parameter.(ones(5)))
+    @variable(model, α[1:5] in MOI.Parameter.(ones(5)))
     @variable(model, x)
     cref = @constraint(model, sum(x for i in 1:5) == sum(2 * α[i] for i in 1:5))
     @objective(model, Min, x)
@@ -653,7 +672,7 @@ end
 
 function test_jump_dual_mixing_params_and_vars_2()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α[1:5] in POI.Parameter.(ones(5)))
+    @variable(model, α[1:5] in MOI.Parameter.(ones(5)))
     @variable(model, x)
     cref = @constraint(model, 0.0 == sum(-x + 2 * α[i] for i in 1:5))
     @objective(model, Min, x)
@@ -666,7 +685,7 @@ end
 
 function test_jump_dual_mixing_params_and_vars_3()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α[1:5] in POI.Parameter.(ones(5)))
+    @variable(model, α[1:5] in MOI.Parameter.(ones(5)))
     @variable(model, x)
     cref = @constraint(model, 0.0 == sum(-x + 2.0 + 2 * α[i] for i in 1:5))
     @objective(model, Min, x)
@@ -679,7 +698,7 @@ end
 
 function test_jump_dual_add_after_solve()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α in POI.Parameter(1.0))
+    @variable(model, α in MOI.Parameter(1.0))
     MOI.set(model, POI.ParameterValue(), α, -1.0)
     @variable(model, x)
     cref = @constraint(model, x <= α)
@@ -688,7 +707,7 @@ function test_jump_dual_add_after_solve()
     @test JuMP.value(x) == -1.0
     @test JuMP.dual(cref) == -1.0
     @test MOI.get(model, POI.ParameterDual(), α) == -1.0
-    @variable(model, b in POI.Parameter(-2.0))
+    @variable(model, b in MOI.Parameter(-2.0))
     cref = @constraint(model, x <= b)
     JuMP.optimize!(model)
     @test JuMP.value(x) == -2.0
@@ -700,7 +719,7 @@ end
 
 function test_jump_dual_add_ctr_alaternative()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α in POI.Parameter(-1.0))
+    @variable(model, α in MOI.Parameter(-1.0))
     @variable(model, x)
     exp = x - α
     cref = @constraint(model, exp ≤ 0)
@@ -714,7 +733,7 @@ end
 
 function test_jump_dual_delete_constraint()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, α in POI.Parameter(-1.0))
+    @variable(model, α in MOI.Parameter(-1.0))
     @variable(model, x)
     cref1 = @constraint(model, x ≤ α / 2)
     cref2 = @constraint(model, x ≤ α)
@@ -749,7 +768,7 @@ function test_jump_nlp()
     model = Model(() -> POI_cached_optimizer())
     @variable(model, x)
     @variable(model, y)
-    @variable(model, z in ParametricOptInterface.Parameter(10))
+    @variable(model, z in MOI.Parameter(10.0))
     @constraint(model, x + y >= z)
     @NLobjective(model, Min, x^2 + y^2)
     optimize!(model)
@@ -764,7 +783,7 @@ function test_jump_nlp()
     MOI.set(ipopt, MOI.RawOptimizerAttribute("print_level"), 0)
     model = Model(() -> ParametricOptInterface.Optimizer(ipopt))
     @variable(model, x)
-    @variable(model, z in ParametricOptInterface.Parameter(10))
+    @variable(model, z in MOI.Parameter(10.0))
     MOI.set(
         model,
         ParametricOptInterface.ConstraintsInterpretation(),
@@ -803,7 +822,7 @@ function test_jump_direct_vector_parameter_affine_nonnegatives()
     set_silent(model)
     @variable(model, x)
     @variable(model, y)
-    @variable(model, t in POI.Parameter(5))
+    @variable(model, t in MOI.Parameter(5.0))
     @constraint(model, [(x - t + 1), (y - t + 2)...] in MOI.Nonnegatives(2))
     @objective(model, Min, x + y)
     optimize!(model)
@@ -839,7 +858,7 @@ function test_jump_direct_vector_parameter_affine_nonpositives()
     set_silent(model)
     @variable(model, x)
     @variable(model, y)
-    @variable(model, t in POI.Parameter(5))
+    @variable(model, t in MOI.Parameter(5.0))
     @constraint(model, [(-x + t - 1), (-y + t - 2)...] in MOI.Nonpositives(2))
     @objective(model, Min, x + y)
     optimize!(model)
@@ -881,7 +900,7 @@ function test_jump_direct_soc_parameters()
     @variable(model, x)
     @variable(model, y)
     @variable(model, t)
-    @variable(model, p in POI.Parameter(0))
+    @variable(model, p in MOI.Parameter(0.0))
     @constraint(model, [y - 1 / √2] in MOI.Nonnegatives(1))
     @constraint(model, [t - 1] in MOI.Zeros(1))
     @constraint(model, [t, (x - p), y...] in SecondOrderCone())
@@ -904,7 +923,7 @@ function test_jump_direct_qp_objective()
     MOI.set(model, MOI.Silent(), true)
     @variable(model, x >= 0)
     @variable(model, y >= 0)
-    @variable(model, p in POI.Parameter(1.0))
+    @variable(model, p in MOI.Parameter(1.0))
     @constraint(model, 2x + y <= 4)
     @constraint(model, x + 2y <= 4)
     @objective(model, Max, (x^2 + y^2) / 2)
@@ -1003,7 +1022,7 @@ function test_jump_direct_rsoc_constraints()
     @variable(model, x)
     @variable(model, y)
     @variable(model, t)
-    @variable(model, p in POI.Parameter(0))
+    @variable(model, p in MOI.Parameter(0.0))
     @constraint(model, [y - 1 / √2] in MOI.Nonnegatives(1))
     @constraint(model, [t - 1] in MOI.Zeros(1))
     @constraint(model, [t, x, y - p] in RotatedSecondOrderCone())
@@ -1028,8 +1047,8 @@ function test_jump_quadratic_interval()
     MOI.set(model, MOI.Silent(), true)
     @variable(model, x >= 0)
     @variable(model, y >= 0)
-    @variable(model, p in POI.Parameter(10.0))
-    @variable(model, q in POI.Parameter(4.0))
+    @variable(model, p in MOI.Parameter(10.0))
+    @variable(model, q in MOI.Parameter(4.0))
     @constraint(model, 0 <= x - p * y + q <= 0)
     @objective(model, Min, x + y)
     optimize!(model)
@@ -1062,8 +1081,8 @@ function test_jump_quadratic_interval_cached()
     # MOI.set(model, MOI.Silent(), true)
     @variable(model, x >= 0)
     @variable(model, y >= 0)
-    @variable(model, p in POI.Parameter(10.0))
-    @variable(model, q in POI.Parameter(4.0))
+    @variable(model, p in MOI.Parameter(10.0))
+    @variable(model, q in MOI.Parameter(4.0))
     @constraint(model, 0 <= x - p * y + q <= 0)
     @objective(model, Min, x + y)
     optimize!(model)
@@ -1082,7 +1101,7 @@ end
 
 function test_affine_parametric_objective()
     model = Model(() -> POI.Optimizer(GLPK.Optimizer()))
-    @variable(model, p in POI.Parameter(1.0))
+    @variable(model, p in MOI.Parameter(1.0))
     @variable(model, 0 <= x <= 1)
     @objective(model, Max, (p + 0.5) * x)
     optimize!(model)
diff --git a/test/moi_tests.jl b/test/moi_tests.jl
index 8c9057ef..ef2cba31 100644
--- a/test/moi_tests.jl
+++ b/test/moi_tests.jl
@@ -16,9 +16,9 @@ function test_basic_tests()
     optimizer = POI.Optimizer(GLPK.Optimizer())
     MOI.set(optimizer, MOI.Silent(), true)
     x = MOI.add_variables(optimizer, 2)
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     z = MOI.VariableIndex(4)
-    cz = MOI.ConstraintIndex{MOI.VariableIndex,POI.Parameter}(4)
+    cz = MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{Float64}}(4)
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
@@ -59,12 +59,12 @@ function test_basic_tests()
           MOI.VariableIndex[MOI.VariableIndex(1), MOI.VariableIndex(2)]
     @test MOI.get(optimizer, POI.ListOfParameterIndices()) ==
           POI.ParameterIndex[POI.ParameterIndex(1)]
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(1.0))
     @test_throws ErrorException("Parameter not in the model") MOI.set(
         optimizer,
         MOI.ConstraintSet(),
         cz,
-        POI.Parameter(1.0),
+        MOI.Parameter(1.0),
     )
     MOI.optimize!(optimizer)
     @test MOI.get(optimizer, MOI.ObjectiveValue()) == 2
@@ -112,7 +112,7 @@ function test_basic_special_cases_of_getters()
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 1], x[1], y))
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 2], x[1], y))
@@ -286,7 +286,7 @@ function test_moi_ListOfConstraintTypesPresent()
         first.(
             MOI.add_constrained_variable.(
                 model,
-                POI.Parameter.(ones(Int(N / 2))),
+                MOI.Parameter.(ones(Int(N / 2))),
             ),
         )
 
@@ -299,9 +299,13 @@ function test_moi_ListOfConstraintTypesPresent()
         ),
         MOI.GreaterThan(1.0),
     )
-    list_ctrs_types = MOI.get(model, MOI.ListOfConstraintTypesPresent())
-    @test list_ctrs_types ==
-          [(MOI.ScalarQuadraticFunction{Float64}, MOI.GreaterThan{Float64})]
+    result = MOI.get(model, MOI.ListOfConstraintTypesPresent())
+    expected = [
+        (MOI.ScalarQuadraticFunction{Float64}, MOI.GreaterThan{Float64}),
+        (MOI.VariableIndex, MOI.Parameter{Float64}),
+    ]
+    @test Set(result) == Set(expected)
+    @test length(result) == length(expected)
     return
 end
 
@@ -314,9 +318,9 @@ function test_production_problem_example()
     b2 = 4.0
     x = MOI.add_variables(optimizer, length(c))
     @test typeof(x[1]) == MOI.VariableIndex
-    w, cw = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-    z, cz = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    w, cw = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+    z, cz = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     @test MOI.get(optimizer, MOI.VariablePrimal(), w) == 0
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
@@ -355,9 +359,9 @@ function test_production_problem_example()
     MOI.get(optimizer, MOI.VariablePrimal(), w)
     MOI.get(optimizer, MOI.VariablePrimal(), y)
     MOI.get(optimizer, MOI.VariablePrimal(), z)
-    MOI.set(optimizer, MOI.ConstraintSet(), cw, POI.Parameter(2.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(1.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cz, POI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cw, MOI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cz, MOI.Parameter(1.0))
     MOI.optimize!(optimizer)
     @test MOI.get(optimizer, MOI.VariablePrimal(), w) == 2.0
     @test MOI.get(optimizer, MOI.VariablePrimal(), y) == 1.0
@@ -367,14 +371,14 @@ function test_production_problem_example()
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cy), 5 / 3, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cz), 2 / 3, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cw), -3.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cw, POI.Parameter(0.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cw, MOI.Parameter(0.0))
     MOI.optimize!(optimizer)
     @test MOI.get(optimizer, MOI.VariablePrimal(), w) == 0.0
     @test MOI.get(optimizer, MOI.VariablePrimal(), y) == 1.0
     @test MOI.get(optimizer, MOI.VariablePrimal(), z) == 1.0
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 7, atol = ATOL)
     @test MOI.get.(optimizer, MOI.VariablePrimal(), x) == [1.0, 1.0]
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(-5.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(-5.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 12.0, atol = ATOL)
     @test MOI.get.(optimizer, MOI.VariablePrimal(), x) == [3.0, 0.0]
@@ -392,9 +396,9 @@ function test_production_problem_example_duals()
     b2 = 4.0
     x = MOI.add_variables(optimizer, length(c))
     @test typeof(x[1]) == MOI.VariableIndex
-    w, cw = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-    z, cz = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    w, cw = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+    z, cz = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     @test MOI.get(optimizer, MOI.VariablePrimal(), w) == 0
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
@@ -440,23 +444,23 @@ function test_production_problem_example_duals()
         -0.5 * MOI.get(optimizer, MOI.ConstraintDual(), ci2),
         atol = 1e-4,
     )
-    MOI.set(optimizer, MOI.ConstraintSet(), cw, POI.Parameter(2.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(1.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cz, POI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cw, MOI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cz, MOI.Parameter(1.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 7.0, atol = ATOL)
     @test MOI.get.(optimizer, MOI.VariablePrimal(), x) == [0.0, 1.0]
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cy), 9.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cz), 0.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cw), -2.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cw, POI.Parameter(0.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cw, MOI.Parameter(0.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 3.0, atol = ATOL)
     @test MOI.get.(optimizer, MOI.VariablePrimal(), x) == [0.0, 1.0]
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cy), 9.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cz), 0.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cw), -2.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(-5.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(-5.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 14.0, atol = ATOL)
     @test ≈(
@@ -485,9 +489,9 @@ function test_production_problem_example_parameters_for_duals_and_intervals()
     b2 = 4.0
     x = MOI.add_variables(optimizer, length(c))
     @test typeof(x[1]) == MOI.VariableIndex
-    w, cw = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-    z, cz = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    w, cw = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+    z, cz = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     @test MOI.get(optimizer, MOI.VariablePrimal(), w) == 0
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
@@ -533,23 +537,23 @@ function test_production_problem_example_parameters_for_duals_and_intervals()
         -0.5 * MOI.get(optimizer, MOI.ConstraintDual(), ci2),
         atol = 1e-4,
     )
-    MOI.set(optimizer, MOI.ConstraintSet(), cw, POI.Parameter(2.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(1.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cz, POI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cw, MOI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cz, MOI.Parameter(1.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 7.0, atol = ATOL)
     @test MOI.get.(optimizer, MOI.VariablePrimal(), x) == [0.0, 1.0]
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cy), 9.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cz), 0.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cw), -2.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cw, POI.Parameter(0.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cw, MOI.Parameter(0.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 3.0, atol = ATOL)
     @test MOI.get.(optimizer, MOI.VariablePrimal(), x) == [0.0, 1.0]
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cy), 9.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cz), 0.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.ConstraintDual(), cw), -2.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(-5.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(-5.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 14.0, atol = ATOL)
     @test ≈(
@@ -581,7 +585,7 @@ function test_vector_parameter_affine_nonnegatives()
     MOI.set(model, MOI.Silent(), true)
     x = MOI.add_variable(model)
     y = MOI.add_variable(model)
-    t, ct = MOI.add_constrained_variable(model, POI.Parameter(5))
+    t, ct = MOI.add_constrained_variable(model, MOI.Parameter(5.0))
     A = [1.0 0 -1; 0 1 -1]
     b = [1.0; 2]
     terms =
@@ -640,7 +644,7 @@ function test_vector_parameter_affine_nonpositives()
     MOI.set(model, MOI.Silent(), true)
     x = MOI.add_variable(model)
     y = MOI.add_variable(model)
-    t, ct = MOI.add_constrained_variable(model, POI.Parameter(5))
+    t, ct = MOI.add_constrained_variable(model, MOI.Parameter(5.0))
     A = [-1.0 0 1; 0 -1 1]
     b = [-1.0; -2]
     terms =
@@ -703,7 +707,7 @@ function test_vector_soc_parameters()
     model = POI.Optimizer(cached)
     MOI.set(model, MOI.Silent(), true)
     x, y, t = MOI.add_variables(model, 3)
-    p, cp = MOI.add_constrained_variable(model, POI.Parameter(0))
+    p, cp = MOI.add_constrained_variable(model, MOI.Parameter(0.0))
     MOI.set(
         model,
         MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
@@ -911,7 +915,7 @@ function test_qp_parameter_in_affine_constraint()
     G = [2.0 3.0 1.0; 1.0 1.0 1.0]
     h = [4.0; 3.0]
     x = MOI.add_variables(optimizer, 2)
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     for i in 1:2
         for j in i:2 # indexes (i,j), (j,i) will be mirrored. specify only one kind
@@ -943,7 +947,7 @@ function test_qp_parameter_in_affine_constraint()
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 12.5, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[1]), 5.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[2]), -2.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(1.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 5.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[1]), 3.0, atol = ATOL)
@@ -962,8 +966,8 @@ function test_qp_parameter_in_quadratic_constraint()
     G = [2.0 3.0 1.0 0.0; 1.0 1.0 0.0 1.0]
     h = [4.0; 3.0]
     x = MOI.add_variables(optimizer, 2)
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-    w, cw = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+    w, cw = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     for i in 1:2
         for j in i:2 # indexes (i,j), (j,i) will be mirrored. specify only one kind
@@ -1001,8 +1005,8 @@ function test_qp_parameter_in_quadratic_constraint()
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 12.5, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[1]), 5.0, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[2]), -2.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(1.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cw, POI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cw, MOI.Parameter(2.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 5.7142, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[1]), 2.1428, atol = ATOL)
@@ -1027,7 +1031,7 @@ function test_qp_variable_times_variable_plus_parameter()
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 1], x[1], x[1]))
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 2], x[1], x[2]))
@@ -1056,7 +1060,7 @@ function test_qp_variable_times_variable_plus_parameter()
         -MOI.get(optimizer, MOI.ConstraintDual(), cons_index),
         atol = ATOL,
     )
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(2.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 8.6609, atol = ATOL)
     return
@@ -1075,7 +1079,7 @@ function test_qp_variable_times_variable_plus_parameter_duals()
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 1], x[1], x[1]))
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 2], x[1], x[2]))
@@ -1106,7 +1110,7 @@ function test_qp_variable_times_variable_plus_parameter_duals()
         -2 * MOI.get(optimizer, MOI.ConstraintDual(), cons_index),
         atol = ATOL,
     )
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(2.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 8.2376, atol = ATOL)
     return
@@ -1126,7 +1130,7 @@ function test_qp_parameter_times_variable()
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
     MOI.add_constraint(optimizer, x[1], MOI.LessThan(20.0))
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 1], x[1], x[1]))
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 2], x[1], y))
@@ -1149,7 +1153,7 @@ function test_qp_parameter_times_variable()
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 30.25, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[1]), 0.5, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[2]), 29.25, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(2.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 22.0, atol = ATOL)
     return
@@ -1169,7 +1173,7 @@ function test_qp_variable_times_parameter()
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
     MOI.add_constraint(optimizer, x[1], MOI.LessThan(20.0))
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[2, 2], y, y))
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 2], y, x[1]))
@@ -1192,7 +1196,7 @@ function test_qp_variable_times_parameter()
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 30.25, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[1]), 0.5, atol = ATOL)
     @test ≈(MOI.get(optimizer, MOI.VariablePrimal(), x[2]), 29.25, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(2.0))
     MOI.optimize!(optimizer)
     @test ≈(MOI.get(optimizer, MOI.ObjectiveValue()), 22.0, atol = ATOL)
     return
@@ -1212,8 +1216,8 @@ function test_qp_parameter_times_parameter()
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
     MOI.add_constraint(optimizer, x[1], MOI.LessThan(20.0))
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
-    z, cz = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
+    z, cz = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 1], y, y))
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 2], y, z))
@@ -1244,14 +1248,14 @@ function test_qp_parameter_times_parameter()
         10.0,
         atol = ATOL,
     )
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(2.0))
     MOI.optimize!(optimizer)
     @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 42.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cz, POI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cz, MOI.Parameter(1.0))
     MOI.optimize!(optimizer)
     @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 36.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(-1.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cz, POI.Parameter(-1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(-1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cz, MOI.Parameter(-1.0))
     MOI.optimize!(optimizer)
     @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 45.0, atol = ATOL)
     return
@@ -1268,7 +1272,7 @@ function test_qp_quadratic_constant()
     G = [2.0 3.0; 1.0 1.0]
     h = [4.0; 3.0]
     x = MOI.add_variables(optimizer, 2)
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(0))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     for i in 1:2
         for j in i:2 # indexes (i,j), (j,i) will be mirrored. specify only one kind
@@ -1311,7 +1315,7 @@ function test_qp_quadratic_constant()
         -2.0,
         atol = ATOL,
     )
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(1.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(1.0))
     MOI.optimize!(optimizer)
     # @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 5.7142, atol = ATOL)
     # @test isapprox.(MOI.get(optimizer, MOI.VariablePrimal(), x[1]), 2.1428, atol = ATOL)
@@ -1330,8 +1334,8 @@ function test_qp_objective_parameter_times_parameter()
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(1))
-    z, cz = MOI.add_constrained_variable(optimizer, POI.Parameter(1))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(1.0))
+    z, cz = MOI.add_constrained_variable(optimizer, MOI.Parameter(1.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     push!(quad_terms, MOI.ScalarQuadraticTerm(1.0, y, z))
     objective_function = MOI.ScalarQuadraticFunction(
@@ -1356,10 +1360,10 @@ function test_qp_objective_parameter_times_parameter()
         ErrorException("Cannot compute the dual of a multiplicative parameter")
     @test_throws err MOI.get(optimizer, MOI.ConstraintDual(), cy)
     @test_throws err MOI.get(optimizer, MOI.ConstraintDual(), cz)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(2.0))
     MOI.optimize!(optimizer)
     @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 2.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cz, POI.Parameter(3.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cz, MOI.Parameter(3.0))
     MOI.optimize!(optimizer)
     @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 6.0, atol = ATOL)
     MOI.set(optimizer, POI.ParameterValue(), y, 5)
@@ -1386,8 +1390,8 @@ function test_qp_objective_affine_parameter()
     for x_i in x
         MOI.add_constraint(optimizer, x_i, MOI.GreaterThan(0.0))
     end
-    y, cy = MOI.add_constrained_variable(optimizer, POI.Parameter(1))
-    z, cz = MOI.add_constrained_variable(optimizer, POI.Parameter(1))
+    y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(1.0))
+    z, cz = MOI.add_constrained_variable(optimizer, MOI.Parameter(1.0))
     quad_terms = MOI.ScalarQuadraticTerm{Float64}[]
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 1], x[1], x[1]))
     push!(quad_terms, MOI.ScalarQuadraticTerm(A[1, 2], x[1], x[2]))
@@ -1410,14 +1414,14 @@ function test_qp_objective_affine_parameter()
         0,
         atol = ATOL,
     )
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(2.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(2.0))
     MOI.optimize!(optimizer)
     @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 5.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cz, POI.Parameter(3.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cz, MOI.Parameter(3.0))
     MOI.optimize!(optimizer)
     @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 7.0, atol = ATOL)
-    MOI.set(optimizer, MOI.ConstraintSet(), cy, POI.Parameter(5.0))
-    MOI.set(optimizer, MOI.ConstraintSet(), cz, POI.Parameter(5.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cy, MOI.Parameter(5.0))
+    MOI.set(optimizer, MOI.ConstraintSet(), cz, MOI.Parameter(5.0))
     MOI.optimize!(optimizer)
     @test isapprox(MOI.get(optimizer, MOI.ObjectiveValue()), 15.0, atol = ATOL)
     return
@@ -1429,7 +1433,7 @@ function test_qp_objective_parameter_in_quadratic_part()
     x = MOI.add_variable(model)
     y = MOI.add_variable(model)
     z = MOI.add_variable(model)
-    p = first(MOI.add_constrained_variable.(model, POI.Parameter(1.0)))
+    p = first(MOI.add_constrained_variable.(model, MOI.Parameter(1.0)))
     MOI.add_constraint(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, y, MOI.GreaterThan(0.0))
     cons1 =
@@ -1479,7 +1483,7 @@ function test_qp_objective_parameter_in_quadratic_part()
     MOI.set(model, MOI.Silent(), true)
     x = MOI.add_variable(model)
     y = MOI.add_variable(model)
-    p = first(MOI.add_constrained_variable.(model, POI.Parameter(1.0)))
+    p = first(MOI.add_constrained_variable.(model, MOI.Parameter(1.0)))
     MOI.add_constraint(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, y, MOI.GreaterThan(0.0))
     cons1 =
@@ -1517,7 +1521,7 @@ function test_qp_objective_parameter_in_quadratic_part()
     MOI.set(model, MOI.Silent(), true)
     x = MOI.add_variable(model)
     y = MOI.add_variable(model)
-    p = first(MOI.add_constrained_variable.(model, POI.Parameter(1.0)))
+    p = first(MOI.add_constrained_variable.(model, MOI.Parameter(1.0)))
     MOI.add_constraint(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, y, MOI.GreaterThan(0.0))
     cons1 =
@@ -1543,7 +1547,7 @@ function test_qp_objective_parameter_in_quadratic_part()
     MOI.set(model, MOI.Silent(), true)
     x = MOI.add_variable(model)
     y = MOI.add_variable(model)
-    p = first(MOI.add_constrained_variable.(model, POI.Parameter(1.0)))
+    p = first(MOI.add_constrained_variable.(model, MOI.Parameter(1.0)))
     MOI.add_constraint(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, y, MOI.GreaterThan(0.0))
     cons1 =