diff --git a/Lib/test/test_bytes.py b/Lib/test/test_bytes.py
index 30000bd9905..f84462891ff 100644
--- a/Lib/test/test_bytes.py
+++ b/Lib/test/test_bytes.py
@@ -277,13 +277,6 @@ class BaseBytesTest(unittest.TestCase):
         self.assertEqual(self.type2test(b".").join([b"ab", b"cd"]), b"ab.cd")
         # XXX more...
 
-    def test_index(self):
-        b = self.type2test(b'parrot')
-        self.assertEqual(b.index('p'), 0)
-        self.assertEqual(b.index('rr'), 2)
-        self.assertEqual(b.index('t'), 5)
-        self.assertRaises(ValueError, lambda: b.index('w'))
-
     def test_count(self):
         b = self.type2test(b'mississippi')
         self.assertEqual(b.count(b'i'), 4)
@@ -369,6 +362,10 @@ class BaseBytesTest(unittest.TestCase):
     def test_split_string_error(self):
         self.assertRaises(TypeError, self.type2test(b'a b').split, ' ')
 
+    def test_split_unicodewhitespace(self):
+        b = self.type2test(b"\x09\x0A\x0B\x0C\x0D\x1C\x1D\x1E\x1F")
+        self.assertEqual(b.split(), [b'\x1c\x1d\x1e\x1f'])
+
     def test_rsplit(self):
         b = self.type2test(b'mississippi')
         self.assertEqual(b.rsplit(b'i'), [b'm', b'ss', b'ss', b'pp', b''])
@@ -392,18 +389,18 @@ class BaseBytesTest(unittest.TestCase):
 
     def test_rsplit_unicodewhitespace(self):
         b = self.type2test(b"\x09\x0A\x0B\x0C\x0D\x1C\x1D\x1E\x1F")
-        self.assertEqual(b.split(), [b'\x1c\x1d\x1e\x1f'])
         self.assertEqual(b.rsplit(), [b'\x1c\x1d\x1e\x1f'])
 
     def test_partition(self):
         b = self.type2test(b'mississippi')
         self.assertEqual(b.partition(b'ss'), (b'mi', b'ss', b'issippi'))
-        self.assertEqual(b.rpartition(b'w'), (b'', b'', b'mississippi'))
+        self.assertEqual(b.partition(b'w'), (b'mississippi', b'', b''))
 
     def test_rpartition(self):
         b = self.type2test(b'mississippi')
         self.assertEqual(b.rpartition(b'ss'), (b'missi', b'ss', b'ippi'))
         self.assertEqual(b.rpartition(b'i'), (b'mississipp', b'i', b''))
+        self.assertEqual(b.rpartition(b'w'), (b'', b'', b'mississippi'))
 
     def test_pickling(self):
         for proto in range(pickle.HIGHEST_PROTOCOL + 1):