diff --git a/src/datatype.c b/src/datatype.c
index 984094f77ffb1..7e78ba8a6901c 100644
--- a/src/datatype.c
+++ b/src/datatype.c
@@ -96,6 +96,7 @@ jl_datatype_t *jl_new_uninitialized_datatype(void)
     t->zeroinit = 0;
     t->isinlinealloc = 0;
     t->has_concrete_subtype = 1;
+    t->cached_by_hash = 0;
     t->layout = NULL;
     t->names = NULL;
     t->types = NULL;
diff --git a/src/dump.c b/src/dump.c
index bce695cd98582..b0403e3620fa5 100644
--- a/src/dump.c
+++ b/src/dump.c
@@ -278,7 +278,8 @@ static void jl_serialize_datatype(jl_serializer_state *s, jl_datatype_t *dt) JL_
             | (dt->isbitstype << 3)
             | (dt->zeroinit << 4)
             | (dt->isinlinealloc << 5)
-            | (dt->has_concrete_subtype << 6));
+            | (dt->has_concrete_subtype << 6)
+            | (dt->cached_by_hash << 7));
     if (!dt->abstract) {
         write_uint16(s->s, dt->ninitialized);
     }
@@ -1174,6 +1175,7 @@ static jl_value_t *jl_deserialize_datatype(jl_serializer_state *s, int pos, jl_v
     dt->zeroinit = (memflags >> 4) & 1;
     dt->isinlinealloc = (memflags >> 5) & 1;
     dt->has_concrete_subtype = (memflags >> 6) & 1;
+    dt->cached_by_hash = (memflags >> 7) & 1;
     dt->types = NULL;
     dt->parameters = NULL;
     dt->name = NULL;
diff --git a/src/jltypes.c b/src/jltypes.c
index 5632a58e35f8a..23d565349d93c 100644
--- a/src/jltypes.c
+++ b/src/jltypes.c
@@ -568,7 +568,8 @@ static int typekey_eq(jl_datatype_t *tt, jl_value_t **key, size_t n)
             // require exact same Type{T}. see e.g. issue #22842
             if (jl_is_type_type(tj) || jl_is_type_type(kj))
                 return 0;
-            if (jl_is_concrete_type(tj) || jl_is_concrete_type(kj))
+            if ((jl_is_concrete_type(tj) || jl_is_concrete_type(kj)) &&
+                jl_type_equality_is_identity(tj, kj))
                 return 0;
             if (!jl_types_equal(tj, kj))
                 return 0;
@@ -860,6 +861,17 @@ jl_datatype_t *jl_lookup_cache_type_(jl_datatype_t *type)
     return (jl_datatype_t*)lookup_type(type->name, key, n);
 }
 
+int jl_type_equality_is_identity(jl_value_t *t1, jl_value_t *t2)
+{
+    if (t1 == t2)
+        return 1;
+    if (!jl_is_datatype(t1) || !jl_is_datatype(t2))
+        return 0;
+    jl_datatype_t *dt1 = (jl_datatype_t *) t1;
+    jl_datatype_t *dt2 = (jl_datatype_t *) t2;
+
+    return dt1->cached_by_hash == dt2->cached_by_hash;
+}
 
 // type instantiation
 
@@ -1155,6 +1167,7 @@ void jl_precompute_memoized_dt(jl_datatype_t *dt, int cacheable)
     if (dt->name == jl_type_typename)
         cacheable = 0; // the cache for Type ignores parameter normalization, so it can't be used as a regular hash
     dt->hash = typekey_hash(dt->name, jl_svec_data(dt->parameters), l, cacheable);
+    dt->cached_by_hash = cacheable ? (typekey_hash(dt->name, jl_svec_data(dt->parameters), l, 0) != 0) : (dt->hash != 0);
 }
 
 static void check_datatype_parameters(jl_typename_t *tn, jl_value_t **params, size_t np)
@@ -1880,7 +1893,7 @@ void jl_init_types(void) JL_GC_DISABLED
     jl_datatype_type->name->wrapper = (jl_value_t*)jl_datatype_type;
     jl_datatype_type->super = (jl_datatype_t*)jl_type_type;
     jl_datatype_type->parameters = jl_emptysvec;
-    jl_datatype_type->name->names = jl_perm_symsvec(19,
+    jl_datatype_type->name->names = jl_perm_symsvec(20,
                                                     "name",
                                                     "super",
                                                     "parameters",
@@ -1899,8 +1912,9 @@ void jl_init_types(void) JL_GC_DISABLED
                                                     "isbitstype",
                                                     "zeroinit",
                                                     "isinlinealloc",
-                                                    "has_concrete_subtype");
-    jl_datatype_type->types = jl_svec(19,
+                                                    "has_concrete_subtype",
+                                                    "cached_by_hash");
+    jl_datatype_type->types = jl_svec(20,
                                       jl_typename_type,
                                       jl_datatype_type,
                                       jl_simplevector_type,
@@ -1909,7 +1923,7 @@ void jl_init_types(void) JL_GC_DISABLED
                                       jl_any_type, jl_any_type, jl_any_type, jl_any_type, // properties
                                       jl_any_type, jl_any_type, jl_any_type, jl_any_type,
                                       jl_any_type, jl_any_type, jl_any_type, jl_any_type,
-                                      jl_any_type);
+                                      jl_any_type, jl_any_type);
     jl_datatype_type->abstract = 0;
     // NOTE: types are not actually mutable, but we want to ensure they are heap-allocated with stable addresses
     jl_datatype_type->mutabl = 1;
@@ -2019,10 +2033,12 @@ void jl_init_types(void) JL_GC_DISABLED
     jl_anytuple_type->isconcretetype = 0;
     jl_anytuple_type->layout = NULL;
     jl_anytuple_type->size = 0;
+    jl_anytuple_type->cached_by_hash = 0;
 
     jl_tvar_t *tttvar = tvar("T");
     ((jl_datatype_t*)jl_type_type)->parameters = jl_svec(1, tttvar);
     ((jl_datatype_t*)jl_type_type)->hasfreetypevars = 1;
+    ((jl_datatype_t*)jl_type_type)->cached_by_hash = 0;
     jl_type_typename->wrapper = jl_new_struct(jl_unionall_type, tttvar, (jl_value_t*)jl_type_type);
     jl_type_type = (jl_unionall_t*)jl_type_typename->wrapper;
 
@@ -2482,6 +2498,7 @@ void jl_init_types(void) JL_GC_DISABLED
     jl_svecset(jl_datatype_type->types, 16, jl_bool_type);
     jl_svecset(jl_datatype_type->types, 17, jl_bool_type);
     jl_svecset(jl_datatype_type->types, 18, jl_bool_type);
+    jl_svecset(jl_datatype_type->types, 19, jl_bool_type);
     jl_svecset(jl_typename_type->types, 1, jl_module_type);
     jl_svecset(jl_typename_type->types, 6, jl_long_type);
     jl_svecset(jl_typename_type->types, 3, jl_type_type);
diff --git a/src/julia.h b/src/julia.h
index c6de10f286da0..4d169c9048f52 100644
--- a/src/julia.h
+++ b/src/julia.h
@@ -457,6 +457,7 @@ typedef struct _jl_datatype_t {
     uint8_t zeroinit; // if one or more fields requires zero-initialization
     uint8_t isinlinealloc; // if this is allocated inline
     uint8_t has_concrete_subtype; // If clear, no value will have this datatype
+    uint8_t cached_by_hash; // stored in hash-based set cache (instead of linear cache)
 } jl_datatype_t;
 
 typedef struct {
@@ -1216,6 +1217,7 @@ JL_DLLEXPORT int jl_egal(jl_value_t *a JL_MAYBE_UNROOTED, jl_value_t *b JL_MAYBE
 JL_DLLEXPORT uintptr_t jl_object_id(jl_value_t *v) JL_NOTSAFEPOINT;
 
 // type predicates and basic operations
+JL_DLLEXPORT int jl_type_equality_is_identity(jl_value_t *t1, jl_value_t *t2) JL_NOTSAFEPOINT;
 JL_DLLEXPORT int jl_has_free_typevars(jl_value_t *v) JL_NOTSAFEPOINT;
 JL_DLLEXPORT int jl_has_typevar(jl_value_t *t, jl_tvar_t *v) JL_NOTSAFEPOINT;
 JL_DLLEXPORT int jl_has_typevar_from_unionall(jl_value_t *t, jl_unionall_t *ua);
diff --git a/src/subtype.c b/src/subtype.c
index 67657fea4e866..a1fab8e81ed21 100644
--- a/src/subtype.c
+++ b/src/subtype.c
@@ -247,7 +247,8 @@ static int obviously_unequal(jl_value_t *a, jl_value_t *b)
             if (ad->name != bd->name)
                 return 1;
             int istuple = (ad->name == jl_tuple_typename);
-            if (jl_is_concrete_type(a) || jl_is_concrete_type(b)) {
+            if ((jl_is_concrete_type(a) || jl_is_concrete_type(b)) &&
+                jl_type_equality_is_identity(a, b)) {
                 if (!istuple && ad->name != jl_type_typename) // HACK: can't properly normalize Tuple{Float64} == Tuple{<:Float64} like types or Type{T} types
                     return 1;
             }
@@ -313,13 +314,11 @@ static int obviously_disjoint(jl_value_t *a, jl_value_t *b, int specificity)
         return 0;
     if (specificity && a == (jl_value_t*)jl_typeofbottom_type)
         return 0;
-    // TODO: this would be a nice fast-path to have, unfortuanately,
-    //       datatype allocation fails to correctly hash-cons them
-    //       and the subtyping tests include tests for this case
-    //if (jl_is_concrete_type(a) && jl_is_concrete_type(b) &&
-    //    (((jl_datatype_t*)a)->name != jl_tuple_typename ||
-    //     ((jl_datatype_t*)b)->name != jl_tuple_typename))
-    //    return 1;
+    if (jl_is_concrete_type(a) && jl_is_concrete_type(b) &&
+        jl_type_equality_is_identity(a, b) &&
+        (((jl_datatype_t*)a)->name != jl_tuple_typename ||
+         ((jl_datatype_t*)b)->name != jl_tuple_typename))
+        return 1;
     if (jl_is_unionall(a)) a = jl_unwrap_unionall(a);
     if (jl_is_unionall(b)) b = jl_unwrap_unionall(b);
     if (jl_is_datatype(a) && jl_is_datatype(b)) {
@@ -2115,7 +2114,7 @@ JL_DLLEXPORT int jl_isa(jl_value_t *x, jl_value_t *t)
             return 0;
         }
     }
-    if (jl_is_concrete_type(t))
+    if (jl_is_concrete_type(t) && jl_type_equality_is_identity(jl_typeof(x), t))
         return 0;
     return jl_subtype(jl_typeof(x), t);
 }
diff --git a/test/core.jl b/test/core.jl
index d7d1a43632a7d..b104a07c0eea3 100644
--- a/test/core.jl
+++ b/test/core.jl
@@ -7239,6 +7239,17 @@ struct AVL35416{K,V}
 end
 @test AVL35416(Node35416{AVL35416{Integer,AbstractString},Int,String}()) isa AVL35416{Integer,AbstractString}
 
+# issue #31696
+foo31696(x::Int8, y::Int8) = 1
+foo31696(x::T, y::T) where {T <: Int8} = 2
+@test length(methods(foo31696)) == 1
+let T1 = Tuple{Int8}, T2 = Tuple{T} where T<:Int8, a = T1[(1,)], b = T2[(1,)]
+    b .= a
+    @test b[1] == (1,)
+    a .= b
+    @test a[1] == (1,)
+end
+
 # issue #36104
 module M36104
 struct T36104
diff --git a/test/subtype.jl b/test/subtype.jl
index 78f88d8a63a86..a34e172192398 100644
--- a/test/subtype.jl
+++ b/test/subtype.jl
@@ -1358,6 +1358,18 @@ let (t, e) = intersection_env(Tuple{Union{Int,Int8}}, Tuple{T} where T)
     @test e[1] isa TypeVar
 end
 
+# issue #25430
+@test Vector{Tuple{Any}}() isa Vector{Tuple{>:Int}}
+@test Vector{Tuple{>:Int}}() isa Vector{Tuple{Any}}
+@test Vector{Tuple{Any}} == Vector{Tuple{>:Int}}
+@test Vector{Vector{Tuple{Any}}} == Vector{Vector{Tuple{>:Int}}}
+f25430(t::Vector{Tuple{Any}}) = true
+g25430(t::Vector{Tuple{>:Int}}) = true
+@test f25430(Vector{Tuple{>:Int}}())
+@test g25430(Vector{Tuple{Any}}())
+@testintersect(Vector{Tuple{>:Int}}, Vector{Tuple{Any}}, Vector{Tuple{Any}})
+@testintersect(Vector{Vector{Tuple{>:Int}}}, Vector{Vector{Tuple{Any}}}, Vector{Vector{Tuple{Any}}})
+
 # issue #24521
 g24521(::T, ::T) where {T} = T
 @test_throws MethodError g24521(Tuple{Any}, Tuple{T} where T)
@@ -1627,18 +1639,9 @@ end
 @testintersect(Tuple{Type{<:AbstractVector{T}}, Int} where T,
                Tuple{Type{Vector}, Any},
                Union{})
-#@testintersect(Tuple{Type{<:AbstractVector{T}}, Int} where T,
-#               Tuple{Type{Vector{T} where Int<:T<:Int}, Any},
-#               Tuple{Type{Vector{Int}}, Int})
-@test_broken isequal(_type_intersect(Tuple{Type{<:AbstractVector{T}}, Int} where T,
-                                     Tuple{Type{Vector{T} where Int<:T<:Int}, Any}),
-                     Tuple{Type{Vector{Int}}, Int})
-@test isequal_type(_type_intersect(Tuple{Type{<:AbstractVector{T}}, Int} where T,
-                                   Tuple{Type{Vector{T} where Int<:T<:Int}, Any}),
-                   Tuple{Type{Vector{Int}}, Int})
-@test isequal_type(_type_intersect(Tuple{Type{Vector{T} where Int<:T<:Int}, Any},
-                                   Tuple{Type{<:AbstractVector{T}}, Int} where T),
-                   Tuple{Type{Vector{Int}}, Int})
+@testintersect(Tuple{Type{<:AbstractVector{T}}, Int} where T,
+               Tuple{Type{Vector{T} where Int<:T<:Int}, Any},
+               Tuple{Type{Vector{Int}}, Int})
 let X = LinearAlgebra.Symmetric{T, S} where S<:(AbstractArray{U, 2} where U<:T) where T,
     Y = Union{LinearAlgebra.Hermitian{T, S} where S<:(AbstractArray{U, 2} where U<:T) where T,
               LinearAlgebra.Symmetric{T, S} where S<:(AbstractArray{U, 2} where U<:T) where T}