diff --git a/Objects/setobject.c b/Objects/setobject.c
index b37db44..d97dc28 100644
--- a/Objects/setobject.c
+++ b/Objects/setobject.c
@@ -2127,17 +2127,7 @@
 PyObject *
 PyFrozenSet_New(PyObject *iterable)
 {
-	PyObject *args, *result;
-
-	if (iterable == NULL)
-		args = PyTuple_New(0);
-	else
-		args = PyTuple_Pack(1, iterable);
-	if (args == NULL)
-		return NULL;
-	result = frozenset_new(&PyFrozenSet_Type, args, NULL);
-	Py_DECREF(args);
-	return result;
+	return make_new_set(&PyFrozenSet_Type, iterable);
 }
 
 Py_ssize_t
@@ -2153,7 +2143,7 @@
 int
 PySet_Clear(PyObject *set)
 {
-	if (!PyType_IsSubtype(Py_TYPE(set), &PySet_Type)) {
+	if (!PySet_Check(set)) {
 		PyErr_BadInternalCall();
 		return -1;
 	}
@@ -2173,7 +2163,7 @@
 int
 PySet_Discard(PyObject *set, PyObject *key)
 {
-	if (!PyType_IsSubtype(Py_TYPE(set), &PySet_Type)) {
+	if (!PySet_Check(set)) {
 		PyErr_BadInternalCall();
 		return -1;
 	}
@@ -2181,13 +2171,13 @@
 }
 
 int
-PySet_Add(PyObject *set, PyObject *key)
+PySet_Add(PyObject *anyset, PyObject *key)
 {
-	if (!PyType_IsSubtype(Py_TYPE(set), &PySet_Type)) {
+	if (!PyAnySet_Check(anyset)) {
 		PyErr_BadInternalCall();
 		return -1;
 	}
-	return set_add_key((PySetObject *)set, key);
+	return set_add_key((PySetObject *)anyset, key);
 }
 
 int
@@ -2224,7 +2214,7 @@
 PyObject *
 PySet_Pop(PyObject *set)
 {
-	if (!PyType_IsSubtype(Py_TYPE(set), &PySet_Type)) {
+	if (!PySet_Check(set)) {
 		PyErr_BadInternalCall();
 		return NULL;
 	}
@@ -2234,7 +2224,7 @@
 int
 _PySet_Update(PyObject *set, PyObject *iterable)
 {
-	if (!PyType_IsSubtype(Py_TYPE(set), &PySet_Type)) {
+	if (!PySet_Check(set)) {
 		PyErr_BadInternalCall();
 		return -1;
 	}
@@ -2330,7 +2320,6 @@
 	f = PyFrozenSet_New(dup);
 	assert(PySet_Size(f) == 3);
 	assert(PyFrozenSet_CheckExact(f));
-	assertRaises(PySet_Add(f, elem) == -1, PyExc_SystemError);
 	assertRaises(PySet_Discard(f, elem) == -1, PyExc_SystemError);
 	assertRaises(PySet_Pop(f) == NULL, PyExc_SystemError);
 	Py_DECREF(f);