diff --git a/Lib/test/string_tests.py b/Lib/test/string_tests.py
index 180072c..4185b9b 100644
--- a/Lib/test/string_tests.py
+++ b/Lib/test/string_tests.py
@@ -169,12 +169,18 @@
     test('rstrip', '   hello   ', '   hello', None)
     test('strip', 'hello', 'hello', None)
 
-    # strip/lstrip/rstrip with real arg
+    # strip/lstrip/rstrip with str arg
     test('strip', 'xyzzyhelloxyzzy', 'hello', 'xyz')
     test('lstrip', 'xyzzyhelloxyzzy', 'helloxyzzy', 'xyz')
     test('rstrip', 'xyzzyhelloxyzzy', 'xyzzyhello', 'xyz')
     test('strip', 'hello', 'hello', 'xyz')
 
+    # strip/lstrip/rstrip with unicode arg
+    test('strip', 'xyzzyhelloxyzzy', u'hello', u'xyz')
+    test('lstrip', 'xyzzyhelloxyzzy', u'helloxyzzy', u'xyz')
+    test('rstrip', 'xyzzyhelloxyzzy', u'xyzzyhello', u'xyz')
+    test('strip', 'hello', u'hello', u'xyz')
+
     test('swapcase', 'HeLLo cOmpUteRs', 'hEllO CoMPuTErS')
     test('translate', 'xyzabcdef', 'xyzxyz', transtable, 'def')
 
diff --git a/Lib/test/test_unicode.py b/Lib/test/test_unicode.py
index 8e8ddf9..5d73939 100644
--- a/Lib/test/test_unicode.py
+++ b/Lib/test/test_unicode.py
@@ -169,6 +169,24 @@
 test('rstrip', u'   hello   ', u'   hello')
 test('strip', u'hello', u'hello')
 
+# strip/lstrip/rstrip with None arg
+test('strip', u'   hello   ', u'hello', None)
+test('lstrip', u'   hello   ', u'hello   ', None)
+test('rstrip', u'   hello   ', u'   hello', None)
+test('strip', u'hello', u'hello', None)
+
+# strip/lstrip/rstrip with unicode arg
+test('strip', u'xyzzyhelloxyzzy', u'hello', u'xyz')
+test('lstrip', u'xyzzyhelloxyzzy', u'helloxyzzy', u'xyz')
+test('rstrip', u'xyzzyhelloxyzzy', u'xyzzyhello', u'xyz')
+test('strip', u'hello', u'hello', u'xyz')
+
+# strip/lstrip/rstrip with str arg
+test('strip', u'xyzzyhelloxyzzy', u'hello', 'xyz')
+test('lstrip', u'xyzzyhelloxyzzy', u'helloxyzzy', 'xyz')
+test('rstrip', u'xyzzyhelloxyzzy', u'xyzzyhello', 'xyz')
+test('strip', u'hello', u'hello', 'xyz')
+
 test('swapcase', u'HeLLo cOmpUteRs', u'hEllO CoMPuTErS')
 
 if 0: