diff --git a/src/gf.c b/src/gf.c
index a488c09f5ea41..4b77da21d9911 100644
--- a/src/gf.c
+++ b/src/gf.c
@@ -938,14 +938,9 @@ static void jl_compilation_sig(
         int notcalled_func = (i_arg > 0 && i_arg <= 8 && !(definition->called & (1 << (i_arg - 1))) &&
                               !jl_has_free_typevars(decl_i) &&
                               jl_subtype(elt, (jl_value_t*)jl_function_type));
-        if (notcalled_func && (type_i == (jl_value_t*)jl_any_type ||
-                               type_i == (jl_value_t*)jl_function_type ||
-                               (jl_is_uniontype(type_i) && // Base.Callable
-                                ((((jl_uniontype_t*)type_i)->a == (jl_value_t*)jl_function_type &&
-                                  ((jl_uniontype_t*)type_i)->b == (jl_value_t*)jl_type_type) ||
-                                 (((jl_uniontype_t*)type_i)->b == (jl_value_t*)jl_function_type &&
-                                  ((jl_uniontype_t*)type_i)->a == (jl_value_t*)jl_type_type))))) {
-            // and attempt to despecialize types marked Function, Callable, or Any
+        if (notcalled_func && (jl_subtype((jl_value_t*)jl_function_type, type_i))) {
+            // and attempt to despecialize types marked as a supertype of Function (i.e.
+            // Function, Callable, Any, or a Union{Function, T})
             // when called with a subtype of Function but is not called
             if (!*newparams) *newparams = jl_svec_copy(tt->parameters);
             jl_svecset(*newparams, i, (jl_value_t*)jl_function_type);
@@ -1174,15 +1169,9 @@ JL_DLLEXPORT int jl_isa_compileable_sig(
         int notcalled_func = (i_arg > 0 && i_arg <= 8 && !(definition->called & (1 << (i_arg - 1))) &&
                               !jl_has_free_typevars(decl_i) &&
                               jl_subtype(elt, (jl_value_t*)jl_function_type));
-        if (notcalled_func && (type_i == (jl_value_t*)jl_any_type ||
-                               type_i == (jl_value_t*)jl_function_type ||
-                               (jl_is_uniontype(type_i) && // Base.Callable
-                                ((((jl_uniontype_t*)type_i)->a == (jl_value_t*)jl_function_type &&
-                                  ((jl_uniontype_t*)type_i)->b == (jl_value_t*)jl_type_type) ||
-                                 (((jl_uniontype_t*)type_i)->b == (jl_value_t*)jl_function_type &&
-                                  ((jl_uniontype_t*)type_i)->a == (jl_value_t*)jl_type_type))))) {
-            // and attempt to despecialize types marked Function, Callable, or Any
-            // when called with a subtype of Function but is not called
+        if (notcalled_func && jl_subtype((jl_value_t*)jl_function_type, type_i)) {
+            // and attempt to despecialize types marked as a supertype of Function (i.e.
+            // Function, Callable, Any, or a Union{Function, T})
             if (elt == (jl_value_t*)jl_function_type)
                 continue;
             JL_GC_POP();
diff --git a/test/core.jl b/test/core.jl
index 4ccf4e15d1acd..5879587943726 100644
--- a/test/core.jl
+++ b/test/core.jl
@@ -233,6 +233,62 @@ k11840(::Type{Union{Tuple{Int32}, Tuple{Int64}}}) = '2'
 @test k11840(Tuple{Union{Int32, Int64}}) == '2'
 @test k11840(Union{Tuple{Int32}, Tuple{Int64}}) == '2'
 
+# issue #59327
+@noinline f59327(f, x) = Any[f, x]
+g59327(x) = f59327(+, Any[x][1])
+g59327(1)
+@test any(
+    mi->mi isa Core.MethodInstance && mi.specTypes == Tuple{typeof(f59327), Function, Int},
+    methods(f59327)[1].specializations)
+
+@noinline h59327(f::Union{Function, Nothing}, x) = Any[f, x]
+i59327(x) = h59327(+, Any[x][1])
+i59327(1)
+@test any(
+    mi->mi isa Core.MethodInstance && mi.specTypes == Tuple{typeof(h59327), Function, Int},
+    methods(h59327)[1].specializations)
+
+@noinline j59327(f::Function, x) = Any[f, x]
+k59327(x) = j59327(+, Any[x][1])
+k59327(1)
+@test any(
+    mi->mi isa Core.MethodInstance && mi.specTypes == Tuple{typeof(j59327), Function, Int},
+    methods(j59327)[1].specializations
+)
+
+@noinline l59327(f::Base.Callable, x) = Any[f, x]
+m59327(x) = l59327(+, Any[x][1])
+m59327(1)
+@test any(
+    mi->mi isa Core.MethodInstance && mi.specTypes == Tuple{typeof(l59327), Function, Int},
+    methods(l59327)[1].specializations
+)
+
+# _do_ specialize if the signature has a `where`
+@noinline n59327(f::F, x) where F = Any[f, x]
+o59327(x) = n59327(+, Any[x][1])
+o59327(1)
+@test !any(
+    mi->mi isa Core.MethodInstance && mi.specTypes == Tuple{typeof(n59327), Function, Int},
+    methods(n59327)[1].specializations
+)
+@test any(
+    mi->mi isa Core.MethodInstance && mi.specTypes == Tuple{typeof(n59327), typeof(+), Int},
+    methods(n59327)[1].specializations
+)
+
+# _do_ specialize if the signature is specific
+@noinline n59327(f::typeof(+), x) = Any[f, x]
+o59327(x) = n59327(+, Any[x][1])
+o59327(1)
+@test !any(
+    mi->mi isa Core.MethodInstance && mi.specTypes == Tuple{typeof(n59327), Function, Int},
+    methods(n59327)[1].specializations
+)
+@test any(
+    mi->mi isa Core.MethodInstance && mi.specTypes == Tuple{typeof(n59327), typeof(+), Int},
+    methods(n59327)[1].specializations
+)
 
 # issue #20511
 f20511(x::DataType) = 0