diff --git a/src/MOI_wrapper.jl b/src/MOI_wrapper.jl
index b8bbf63..853fa86 100644
--- a/src/MOI_wrapper.jl
+++ b/src/MOI_wrapper.jl
@@ -149,6 +149,17 @@ function MOI.is_valid(model::Optimizer, vi::MOI.VariableIndex)
     return false
 end
 
+function MOI.is_valid(
+    model::Optimizer,
+    ci::MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{T}},
+) where {T}
+    vi = MOI.VariableIndex(ci.value)
+    if haskey(model.parameters, p_idx(vi))
+        return true
+    end
+    return false
+end
+
 function MOI.supports(
     model::Optimizer,
     attr::MOI.VariableName,
diff --git a/test/moi_tests.jl b/test/moi_tests.jl
index 6e3350c..29d40bd 100644
--- a/test/moi_tests.jl
+++ b/test/moi_tests.jl
@@ -19,6 +19,7 @@ function test_basic_tests()
     y, cy = MOI.add_constrained_variable(optimizer, MOI.Parameter(0.0))
     @test MOI.is_valid(optimizer, x[1])
     @test MOI.is_valid(optimizer, y)
+    @test MOI.is_valid(optimizer, cy)
     @test MOI.get(optimizer, POI.ListOfPureVariableIndices()) == x
     @test MOI.get(optimizer, MOI.ListOfVariableIndices()) == [x[1], x[2], y]
     z = MOI.VariableIndex(4)