diff --git a/Lib/test/string_tests.py b/Lib/test/string_tests.py
index a813616..09622dd 100644
--- a/Lib/test/string_tests.py
+++ b/Lib/test/string_tests.py
@@ -1156,6 +1156,63 @@
         self.checkraises(ValueError, S, 'rpartition', '')
         self.checkraises(TypeError, S, 'rpartition', None)
 
+    def test_none_arguments(self):
+        # issue 11828
+        s = 'hello'
+        self.checkequal(2, s, 'find', 'l', None)
+        self.checkequal(3, s, 'find', 'l', -2, None)
+        self.checkequal(2, s, 'find', 'l', None, -2)
+        self.checkequal(0, s, 'find', 'h', None, None)
+
+        self.checkequal(3, s, 'rfind', 'l', None)
+        self.checkequal(3, s, 'rfind', 'l', -2, None)
+        self.checkequal(2, s, 'rfind', 'l', None, -2)
+        self.checkequal(0, s, 'rfind', 'h', None, None)
+
+        self.checkequal(2, s, 'index', 'l', None)
+        self.checkequal(3, s, 'index', 'l', -2, None)
+        self.checkequal(2, s, 'index', 'l', None, -2)
+        self.checkequal(0, s, 'index', 'h', None, None)
+
+        self.checkequal(3, s, 'rindex', 'l', None)
+        self.checkequal(3, s, 'rindex', 'l', -2, None)
+        self.checkequal(2, s, 'rindex', 'l', None, -2)
+        self.checkequal(0, s, 'rindex', 'h', None, None)
+
+        self.checkequal(2, s, 'count', 'l', None)
+        self.checkequal(1, s, 'count', 'l', -2, None)
+        self.checkequal(1, s, 'count', 'l', None, -2)
+        self.checkequal(0, s, 'count', 'x', None, None)
+
+        self.checkequal(True, s, 'endswith', 'o', None)
+        self.checkequal(True, s, 'endswith', 'lo', -2, None)
+        self.checkequal(True, s, 'endswith', 'l', None, -2)
+        self.checkequal(False, s, 'endswith', 'x', None, None)
+
+        self.checkequal(True, s, 'startswith', 'h', None)
+        self.checkequal(True, s, 'startswith', 'l', -2, None)
+        self.checkequal(True, s, 'startswith', 'h', None, -2)
+        self.checkequal(False, s, 'startswith', 'x', None, None)
+
+    def test_find_etc_raise_correct_error_messages(self):
+        # issue 11828
+        s = 'hello'
+        x = 'x'
+        self.assertRaisesRegexp(TypeError, r'^find\(', s.find,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'^rfind\(', s.rfind,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'^index\(', s.index,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'^rindex\(', s.rindex,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'^count\(', s.count,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'^startswith\(', s.startswith,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'^endswith\(', s.endswith,
+                                x, None, None, None)
+
 
 class MixinStrUnicodeTest:
     # Additional tests that only work with str and unicode.
diff --git a/Lib/test/test_bytes.py b/Lib/test/test_bytes.py
index 8b964ca..a607bef 100644
--- a/Lib/test/test_bytes.py
+++ b/Lib/test/test_bytes.py
@@ -459,6 +459,68 @@
         self.assertRaises(ValueError, self.type2test.maketrans, b'abc', b'xyzq')
         self.assertRaises(TypeError, self.type2test.maketrans, 'abc', 'def')
 
+    def test_none_arguments(self):
+        # issue 11828
+        b = self.type2test(b'hello')
+        l = self.type2test(b'l')
+        h = self.type2test(b'h')
+        x = self.type2test(b'x')
+        o = self.type2test(b'o')
+
+        self.assertEqual(2, b.find(l, None))
+        self.assertEqual(3, b.find(l, -2, None))
+        self.assertEqual(2, b.find(l, None, -2))
+        self.assertEqual(0, b.find(h, None, None))
+
+        self.assertEqual(3, b.rfind(l, None))
+        self.assertEqual(3, b.rfind(l, -2, None))
+        self.assertEqual(2, b.rfind(l, None, -2))
+        self.assertEqual(0, b.rfind(h, None, None))
+
+        self.assertEqual(2, b.index(l, None))
+        self.assertEqual(3, b.index(l, -2, None))
+        self.assertEqual(2, b.index(l, None, -2))
+        self.assertEqual(0, b.index(h, None, None))
+
+        self.assertEqual(3, b.rindex(l, None))
+        self.assertEqual(3, b.rindex(l, -2, None))
+        self.assertEqual(2, b.rindex(l, None, -2))
+        self.assertEqual(0, b.rindex(h, None, None))
+
+        self.assertEqual(2, b.count(l, None))
+        self.assertEqual(1, b.count(l, -2, None))
+        self.assertEqual(1, b.count(l, None, -2))
+        self.assertEqual(0, b.count(x, None, None))
+
+        self.assertEqual(True, b.endswith(o, None))
+        self.assertEqual(True, b.endswith(o, -2, None))
+        self.assertEqual(True, b.endswith(l, None, -2))
+        self.assertEqual(False, b.endswith(x, None, None))
+
+        self.assertEqual(True, b.startswith(h, None))
+        self.assertEqual(True, b.startswith(l, -2, None))
+        self.assertEqual(True, b.startswith(h, None, -2))
+        self.assertEqual(False, b.startswith(x, None, None))
+
+    def test_find_etc_raise_correct_error_messages(self):
+        # issue 11828
+        b = self.type2test(b'hello')
+        x = self.type2test(b'x')
+        self.assertRaisesRegexp(TypeError, r'\bfind\b', b.find,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'\brfind\b', b.rfind,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'\bindex\b', b.index,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'\brindex\b', b.rindex,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'\bcount\b', b.count,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'\bstartswith\b', b.startswith,
+                                x, None, None, None)
+        self.assertRaisesRegexp(TypeError, r'\bendswith\b', b.endswith,
+                                x, None, None, None)
+
 
 class BytesTest(BaseBytesTest):
     type2test = bytes