diff --git a/src/gf.c b/src/gf.c
index c01da4554ef1e..c8f38f44f0f61 100644
--- a/src/gf.c
+++ b/src/gf.c
@@ -415,7 +415,7 @@ JL_DLLEXPORT void jl_set_typeinf_func(jl_value_t *f)
 
 static int very_general_type(jl_value_t *t)
 {
-    return (t == (jl_value_t*)jl_any_type || t == (jl_value_t*)jl_type_type || jl_types_equal(t, (jl_value_t*)jl_type_type));
+    return (t == (jl_value_t*)jl_any_type || jl_types_equal(t, (jl_value_t*)jl_type_type));
 }
 
 jl_value_t *jl_nth_slot_type(jl_value_t *sig, size_t i)
@@ -528,17 +528,17 @@ static void jl_compilation_sig(
             }
         }
 
-        if (jl_types_equal(elt, (jl_value_t*)jl_typetype_type)) {
+        if (jl_types_equal(elt, (jl_value_t*)jl_typetype_type)) { // elt == Type{T} where T
             // not triggered for isdispatchtuple(tt), this attempts to handle
             // some cases of adapting a random signature into a compilation signature
         }
-        else if (!jl_is_datatype(elt) && !jl_has_empty_intersection((jl_value_t*)jl_type_type, elt)) {
+        else if (!jl_is_datatype(elt) && jl_subtype(elt, (jl_value_t*)jl_type_type)) { // elt <: Type{T}
             // not triggered for isdispatchtuple(tt), this attempts to handle
             // some cases of adapting a random signature into a compilation signature
             if (!*newparams) *newparams = jl_svec_copy(tt->parameters);
             jl_svecset(*newparams, i, jl_typetype_type);
         }
-        else if (jl_is_type_type(elt)) {
+        else if (jl_is_type_type(elt)) { // elt isa Type{T}
             if (very_general_type(decl_i)) {
                 /*
                   here's a fairly simple heuristic: if this argument slot's
diff --git a/test/core.jl b/test/core.jl
index 3d561b37948b9..f26e633f35b15 100644
--- a/test/core.jl
+++ b/test/core.jl
@@ -6894,3 +6894,24 @@ function foo31357(b::Bool)
 end
 @test foo31357(true) == 12345
 @test foo31357(false) == 12345
+
+# Issue #31406
+abstract type Shape31406 end
+struct ValueOf31406 <: Shape31406
+    ty::Type
+end
+struct TupleOf31406 <: Shape31406
+    cols::Vector{Shape31406}
+end
+TupleOf31406(cols::Union{Shape31406,Type}...) = TupleOf31406(collect(Shape31406, cols))
+@test (TupleOf31406(ValueOf31406(Int64), ValueOf31406(Float64))::TupleOf31406).cols ==
+    Shape31406[ValueOf31406(Int64), ValueOf31406(Float64)]
+@test try
+        TupleOf31406(ValueOf31406(Int64), Float64)
+        false
+    catch ex
+        if !(ex isa MethodError && ex.f === convert && ex.args == (Shape31406, Float64))
+            rethrow(ex)
+        end
+        true
+    end