diff --git a/Lib/test/string_tests.py b/Lib/test/string_tests.py
index 0d4c7ecf4a04f2..d69edd7bf458da 100644
--- a/Lib/test/string_tests.py
+++ b/Lib/test/string_tests.py
@@ -469,6 +469,11 @@ def test_split(self):
         self.checkraises(ValueError, 'hello', 'split', '', 0)
 
     def test_rsplit(self):
+        # without arg
+        self.checkequal(['a', 'b', 'c', 'd'], 'a b c d', 'rsplit')
+        self.checkequal(['a', 'b', 'c', 'd'], 'a  b  c d', 'rsplit')
+        self.checkequal([], '', 'rsplit')
+
         # by a char
         self.checkequal(['a', 'b', 'c', 'd'], 'a|b|c|d', 'rsplit', '|')
         self.checkequal(['a|b|c', 'd'], 'a|b|c|d', 'rsplit', '|', 1)
@@ -522,6 +527,9 @@ def test_rsplit(self):
 
         # with keyword args
         self.checkequal(['a', 'b', 'c', 'd'], 'a|b|c|d', 'rsplit', sep='|')
+        self.checkequal(['a', 'b', 'c', 'd'], 'a b c d', 'rsplit', sep=None)
+        self.checkequal(['a b c', 'd'],
+                        'a b c d', 'rsplit', sep=None, maxsplit=1)
         self.checkequal(['a|b|c', 'd'],
                         'a|b|c|d', 'rsplit', '|', maxsplit=1)
         self.checkequal(['a|b|c', 'd'],
diff --git a/Lib/test/test_unicode.py b/Lib/test/test_unicode.py
index 9b0e4b230506a8..60e5b1902cf698 100644
--- a/Lib/test/test_unicode.py
+++ b/Lib/test/test_unicode.py
@@ -441,10 +441,10 @@ def test_split(self):
     def test_rsplit(self):
         string_tests.CommonTest.test_rsplit(self)
         # test mixed kinds
-        for left, right in ('ba', '\u0101\u0100', '\U00010301\U00010300'):
+        for left, right in ('ba', 'юё', '\u0101\u0100', '\U00010301\U00010300'):
             left *= 9
             right *= 9
-            for delim in ('c', '\u0102', '\U00010302'):
+            for delim in ('c', 'ы', '\u0102', '\U00010302'):
                 self.checkequal([left + right],
                                 left + right, 'rsplit', delim)
                 self.checkequal([left, right],
@@ -454,6 +454,10 @@ def test_rsplit(self):
                 self.checkequal([left, right],
                                 left + delim * 2 + right, 'rsplit', delim *2)
 
+            # Check `None` as well:
+            self.checkequal([left + right],
+                             left + right, 'rsplit', None)
+
     def test_partition(self):
         string_tests.MixinStrUnicodeUserStringTest.test_partition(self)
         # test mixed kinds