diff --git a/Lib/test/test_email/test_email.py b/Lib/test/test_email/test_email.py
index 5cc6d04..36c344f 100644
--- a/Lib/test/test_email/test_email.py
+++ b/Lib/test/test_email/test_email.py
@@ -2718,8 +2718,17 @@
             utils.formatdate(now, localtime=False, usegmt=True),
             time.strftime('%a, %d %b %Y %H:%M:%S GMT', time.gmtime(now)))
 
-    def test_parsedate_none(self):
-        self.assertEqual(utils.parsedate(''), None)
+    # parsedate and parsedate_tz will become deprecated interfaces someday
+    def test_parsedate_returns_None_for_invalid_strings(self):
+        self.assertIsNone(utils.parsedate(''))
+        self.assertIsNone(utils.parsedate_tz(''))
+        self.assertIsNone(utils.parsedate('0'))
+        self.assertIsNone(utils.parsedate_tz('0'))
+        self.assertIsNone(utils.parsedate('A Complete Waste of Time'))
+        self.assertIsNone(utils.parsedate_tz('A Complete Waste of Time'))
+        # Not a part of the spec but, but this has historically worked:
+        self.assertIsNone(utils.parsedate(None))
+        self.assertIsNone(utils.parsedate_tz(None))
 
     def test_parsedate_compact(self):
         # The FWS after the comma is optional