diff --git a/Lib/test/list_tests.py b/Lib/test/list_tests.py
index 0824d482e24..42e118ba8f8 100644
--- a/Lib/test/list_tests.py
+++ b/Lib/test/list_tests.py
@@ -365,13 +365,6 @@ class CommonTest(seq_tests.CommonTest):
         self.assertEqual(u.index(0, 3), 3)
         self.assertEqual(u.index(0, 3, 4), 3)
         self.assertRaises(ValueError, u.index, 2, 0, -10)
-        self.assertEqual(u.index(1, None), 4)
-        self.assertEqual(u.index(1, None, None), 4)
-        self.assertEqual(u.index(1, 0, None), 4)
-        self.assertEqual(u.index(1, None, 6), 4)
-        self.assertRaises(ValueError, u.index, -1, 3)
-        self.assertRaises(ValueError, u.index, -1, 3, None)
-        self.assertRaises(ValueError, u.index, 1, None, 4)
 
         self.assertRaises(TypeError, u.index)
 
diff --git a/Lib/test/seq_tests.py b/Lib/test/seq_tests.py
index 824ae0191f2..f655c29eee2 100644
--- a/Lib/test/seq_tests.py
+++ b/Lib/test/seq_tests.py
@@ -361,13 +361,6 @@ class CommonTest(unittest.TestCase):
         self.assertEqual(u.index(0, 3), 3)
         self.assertEqual(u.index(0, 3, 4), 3)
         self.assertRaises(ValueError, u.index, 2, 0, -10)
-        self.assertEqual(u.index(1, None), 4)
-        self.assertEqual(u.index(1, None, None), 4)
-        self.assertEqual(u.index(1, 0, None), 4)
-        self.assertEqual(u.index(1, None, 6), 4)
-        self.assertRaises(ValueError, u.index, -1, 3)
-        self.assertRaises(ValueError, u.index, -1, 3, None)
-        self.assertRaises(ValueError, u.index, 1, None, 4)
 
         self.assertRaises(TypeError, u.index)
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 82edaa4f783..73463488679 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -16,9 +16,6 @@ Core and Builtins
 - Issue #13342: input() used to ignore sys.stdin's and sys.stdout's unicode
   error handler in interactive mode (when calling into PyOS_Readline()).
 
-- Issue #13340: Accept None as start and stop parameters for
-  list.index() and tuple.index().
-
 - Issue #9896: Add start, stop, and step attributes to range objects.
 
 - Issue #13343: Fix a SystemError when a lambda expression uses a global
diff --git a/Objects/listobject.c b/Objects/listobject.c
index cf4f2766d57..69a632d5289 100644
--- a/Objects/listobject.c
+++ b/Objects/listobject.c
@@ -2122,19 +2122,11 @@ listindex(PyListObject *self, PyObject *args)
 {
     Py_ssize_t i, start=0, stop=Py_SIZE(self);
     PyObject *v;
-    PyObject *start_obj = NULL, *stop_obj = NULL;
 
-    if (!PyArg_ParseTuple(args, "O|OO:index", &v, &start_obj, &stop_obj))
+    if (!PyArg_ParseTuple(args, "O|O&O&:index", &v,
+                                _PyEval_SliceIndex, &start,
+                                _PyEval_SliceIndex, &stop))
         return NULL;
-
-    if (start_obj != Py_None)
-        if (!_PyEval_SliceIndex(start_obj, &start))
-            return NULL;
-
-    if (stop_obj != Py_None)
-        if (!_PyEval_SliceIndex(stop_obj, &stop))
-            return NULL;
-
     if (start < 0) {
         start += Py_SIZE(self);
         if (start < 0)
diff --git a/Objects/tupleobject.c b/Objects/tupleobject.c
index e311fcca5d2..54a580d4a33 100644
--- a/Objects/tupleobject.c
+++ b/Objects/tupleobject.c
@@ -484,19 +484,12 @@ static PyObject *
 tupleindex(PyTupleObject *self, PyObject *args)
 {
     Py_ssize_t i, start=0, stop=Py_SIZE(self);
-    PyObject *v, *start_obj = NULL, *stop_obj = NULL;
+    PyObject *v;
 
-    if (!PyArg_ParseTuple(args, "O|OO:index", &v, &start_obj, &stop_obj))
+    if (!PyArg_ParseTuple(args, "O|O&O&:index", &v,
+                                _PyEval_SliceIndex, &start,
+                                _PyEval_SliceIndex, &stop))
         return NULL;
-
-    if (start_obj != Py_None)
-        if (!_PyEval_SliceIndex(start_obj, &start))
-            return NULL;
-
-    if (stop_obj != Py_None)
-        if (!_PyEval_SliceIndex(stop_obj, &stop))
-            return NULL;
-
     if (start < 0) {
         start += Py_SIZE(self);
         if (start < 0)