diff --git a/Python/specialize.c b/Python/specialize.c
index 2e135be010ff54..020127e9bf3c99 100644
--- a/Python/specialize.c
+++ b/Python/specialize.c
@@ -394,14 +394,14 @@ _PyCode_Quicken(PyCodeObject *code)
 
 #define SPEC_FAIL_CALL_INSTANCE_METHOD 11
 #define SPEC_FAIL_CALL_CMETHOD 12
-#define SPEC_FAIL_CALL_PYCFUNCTION 13
-#define SPEC_FAIL_CALL_PYCFUNCTION_WITH_KEYWORDS 14
-#define SPEC_FAIL_CALL_PYCFUNCTION_FAST_WITH_KEYWORDS 15
-#define SPEC_FAIL_CALL_PYCFUNCTION_NOARGS 16
+#define SPEC_FAIL_CALL_CFUNC_VARARGS 13
+#define SPEC_FAIL_CALL_CFUNC_VARARGS_KEYWORDS 14
+#define SPEC_FAIL_CALL_CFUNC_FASTCALL_KEYWORDS 15
+#define SPEC_FAIL_CALL_CFUNC_NOARGS 16
 #define SPEC_FAIL_CALL_BAD_CALL_FLAGS 17
-#define SPEC_FAIL_CALL_CLASS 18
+#define SPEC_FAIL_CALL_CFUNC_METHOD_FASTCALL_KEYWORDS 18
 #define SPEC_FAIL_CALL_PYTHON_CLASS 19
-#define SPEC_FAIL_CALL_METHOD_DESCRIPTOR 20
+#define SPEC_FAIL_CALL_PEP_523 20
 #define SPEC_FAIL_CALL_BOUND_METHOD 21
 #define SPEC_FAIL_CALL_STR 22
 #define SPEC_FAIL_CALL_CLASS_NO_VECTORCALL 23
@@ -409,8 +409,6 @@ _PyCode_Quicken(PyCodeObject *code)
 #define SPEC_FAIL_CALL_KWNAMES 25
 #define SPEC_FAIL_CALL_METHOD_WRAPPER 26
 #define SPEC_FAIL_CALL_OPERATOR_WRAPPER 27
-#define SPEC_FAIL_CALL_PYFUNCTION 28
-#define SPEC_FAIL_CALL_PEP_523 29
 
 /* COMPARE_OP */
 #define SPEC_FAIL_COMPARE_OP_DIFFERENT_TYPES 12
@@ -1517,17 +1515,19 @@ builtin_call_fail_kind(int ml_flags)
     switch (ml_flags & (METH_VARARGS | METH_FASTCALL | METH_NOARGS | METH_O |
         METH_KEYWORDS | METH_METHOD)) {
         case METH_VARARGS:
-            return SPEC_FAIL_CALL_PYCFUNCTION;
+            return SPEC_FAIL_CALL_CFUNC_VARARGS;
         case METH_VARARGS | METH_KEYWORDS:
-            return SPEC_FAIL_CALL_PYCFUNCTION_WITH_KEYWORDS;
+            return SPEC_FAIL_CALL_CFUNC_VARARGS_KEYWORDS;
         case METH_FASTCALL | METH_KEYWORDS:
-            return SPEC_FAIL_CALL_PYCFUNCTION_FAST_WITH_KEYWORDS;
+            return SPEC_FAIL_CALL_CFUNC_FASTCALL_KEYWORDS;
         case METH_NOARGS:
-            return SPEC_FAIL_CALL_PYCFUNCTION_NOARGS;
-        /* This case should never happen with PyCFunctionObject -- only
-            PyMethodObject. See zlib.compressobj()'s methods for an example.
-        */
+            return SPEC_FAIL_CALL_CFUNC_NOARGS;
         case METH_METHOD | METH_FASTCALL | METH_KEYWORDS:
+            return SPEC_FAIL_CALL_CFUNC_METHOD_FASTCALL_KEYWORDS;
+        /* These cases should be optimized, but return "other" just in case */
+        case METH_O:
+        case METH_FASTCALL:
+            return SPEC_FAIL_OTHER;
         default:
             return SPEC_FAIL_CALL_BAD_CALL_FLAGS;
     }
@@ -1698,33 +1698,18 @@ specialize_c_call(PyObject *callable, _Py_CODEUNIT *instr, int nargs,
 static int
 call_fail_kind(PyObject *callable)
 {
-    if (PyCFunction_CheckExact(callable)) {
-        return SPEC_FAIL_CALL_PYCFUNCTION;
-    }
-    else if (PyFunction_Check(callable)) {
-        return SPEC_FAIL_CALL_PYFUNCTION;
-    }
-    else if (PyInstanceMethod_Check(callable)) {
+    assert(!PyCFunction_CheckExact(callable));
+    assert(!PyFunction_Check(callable));
+    assert(!PyType_Check(callable));
+    assert(!Py_IS_TYPE(callable, &PyMethodDescr_Type));
+    assert(!PyMethod_Check(callable));
+    if (PyInstanceMethod_Check(callable)) {
         return SPEC_FAIL_CALL_INSTANCE_METHOD;
     }
-    else if (PyMethod_Check(callable)) {
-        return SPEC_FAIL_CALL_BOUND_METHOD;
-    }
     // builtin method
     else if (PyCMethod_Check(callable)) {
         return SPEC_FAIL_CALL_CMETHOD;
     }
-    else if (PyType_Check(callable)) {
-        if (((PyTypeObject *)callable)->tp_new == PyBaseObject_Type.tp_new) {
-            return SPEC_FAIL_CALL_PYTHON_CLASS;
-        }
-        else {
-            return SPEC_FAIL_CALL_CLASS;
-        }
-    }
-    else if (Py_IS_TYPE(callable, &PyMethodDescr_Type)) {
-        return SPEC_FAIL_CALL_METHOD_DESCRIPTOR;
-    }
     else if (Py_TYPE(callable) == &PyWrapperDescr_Type) {
         return SPEC_FAIL_CALL_OPERATOR_WRAPPER;
     }
@@ -1760,7 +1745,7 @@ _Py_Specialize_Call(PyObject *callable, _Py_CODEUNIT *instr, int nargs,
         fail = specialize_method_descriptor((PyMethodDescrObject *)callable,
                                             instr, nargs, kwnames);
     }
-    else if (Py_TYPE(callable) == &PyMethod_Type) {
+    else if (PyMethod_Check(callable)) {
         PyObject *func = ((PyMethodObject *)callable)->im_func;
         if (PyFunction_Check(func)) {
             fail = specialize_py_call((PyFunctionObject *)func,