diff --git a/Lib/test/test_builtin.py b/Lib/test/test_builtin.py
index 103d1a3..52c1fe0 100644
--- a/Lib/test/test_builtin.py
+++ b/Lib/test/test_builtin.py
@@ -582,14 +582,16 @@
         self.assertRaises(TypeError, getattr, sys, 1)
         self.assertRaises(TypeError, getattr, sys, 1, "foo")
         self.assertRaises(TypeError, getattr)
-        self.assertRaises(UnicodeError, getattr, sys, unichr(sys.maxunicode))
+        if have_unicode:
+            self.assertRaises(UnicodeError, getattr, sys, unichr(sys.maxunicode))
 
     def test_hasattr(self):
         import sys
         self.assert_(hasattr(sys, 'stdout'))
         self.assertRaises(TypeError, hasattr, sys, 1)
         self.assertRaises(TypeError, hasattr)
-        self.assertRaises(UnicodeError, hasattr, sys, unichr(sys.maxunicode))
+        if have_unicode:
+            self.assertRaises(UnicodeError, hasattr, sys, unichr(sys.maxunicode))
 
     def test_hash(self):
         hash(None)
@@ -1101,7 +1103,8 @@
         if have_unicode:
             self.assertEqual(ord(unichr(sys.maxunicode)), sys.maxunicode)
         self.assertRaises(TypeError, ord, 42)
-        self.assertRaises(TypeError, ord, unicode("12"))
+        if have_unicode:
+            self.assertRaises(TypeError, ord, unicode("12"))
 
     def test_pow(self):
         self.assertEqual(pow(0,0), 1)
@@ -1494,11 +1497,17 @@
 
     def test_inputtypes(self):
         s = 'abracadabra'
-        for T in [unicode, list, tuple]:
+        types = [list, tuple]
+        if have_unicode:
+            types.insert(0, unicode)
+        for T in types:
             self.assertEqual(sorted(s), sorted(T(s)))
 
         s = ''.join(dict.fromkeys(s).keys())  # unique letters only
-        for T in [unicode, set, frozenset, list, tuple, dict.fromkeys]:
+        types = [set, frozenset, list, tuple, dict.fromkeys]
+        if have_unicode:
+            types.insert(0, unicode)
+        for T in types:
             self.assertEqual(sorted(s), sorted(T(s)))
 
     def test_baddecorator(self):
diff --git a/Lib/test/test_isinstance.py b/Lib/test/test_isinstance.py
index 89ef200..25b0816 100644
--- a/Lib/test/test_isinstance.py
+++ b/Lib/test/test_isinstance.py
@@ -243,7 +243,8 @@
         self.assertEqual(True, issubclass(NewSuper, (NewChild, (NewSuper,))))
 
         self.assertEqual(True, issubclass(int, (long, (float, int))))
-        self.assertEqual(True, issubclass(str, (unicode, (Child, NewChild, basestring))))
+        if test_support.have_unicode:
+            self.assertEqual(True, issubclass(str, (unicode, (Child, NewChild, basestring))))
 
     def test_subclass_recursion_limit(self):
         # make sure that issubclass raises RuntimeError before the C stack is
diff --git a/Lib/test/test_sys.py b/Lib/test/test_sys.py
index e1bb8bf..b98c648 100644
--- a/Lib/test/test_sys.py
+++ b/Lib/test/test_sys.py
@@ -247,7 +247,8 @@
         self.assert_(isinstance(sys.executable, basestring))
         self.assert_(isinstance(sys.hexversion, int))
         self.assert_(isinstance(sys.maxint, int))
-        self.assert_(isinstance(sys.maxunicode, int))
+        if test.test_support.have_unicode:
+            self.assert_(isinstance(sys.maxunicode, int))
         self.assert_(isinstance(sys.platform, basestring))
         self.assert_(isinstance(sys.prefix, basestring))
         self.assert_(isinstance(sys.version, basestring))
diff --git a/Lib/test/test_textwrap.py b/Lib/test/test_textwrap.py
index a21b7ce..68e4d6d 100644
--- a/Lib/test/test_textwrap.py
+++ b/Lib/test/test_textwrap.py
@@ -328,17 +328,18 @@
         self.check_wrap(text, 30,
                         [" This is a sentence with", "leading whitespace."])
 
-    def test_unicode(self):
-        # *Very* simple test of wrapping Unicode strings.  I'm sure
-        # there's more to it than this, but let's at least make
-        # sure textwrap doesn't crash on Unicode input!
-        text = u"Hello there, how are you today?"
-        self.check_wrap(text, 50, [u"Hello there, how are you today?"])
-        self.check_wrap(text, 20, [u"Hello there, how are", "you today?"])
-        olines = self.wrapper.wrap(text)
-        assert isinstance(olines, list) and isinstance(olines[0], unicode)
-        otext = self.wrapper.fill(text)
-        assert isinstance(otext, unicode)
+    if test_support.have_unicode:
+        def test_unicode(self):
+            # *Very* simple test of wrapping Unicode strings.  I'm sure
+            # there's more to it than this, but let's at least make
+            # sure textwrap doesn't crash on Unicode input!
+            text = u"Hello there, how are you today?"
+            self.check_wrap(text, 50, [u"Hello there, how are you today?"])
+            self.check_wrap(text, 20, [u"Hello there, how are", "you today?"])
+            olines = self.wrapper.wrap(text)
+            assert isinstance(olines, list) and isinstance(olines[0], unicode)
+            otext = self.wrapper.fill(text)
+            assert isinstance(otext, unicode)
 
     def test_split(self):
         # Ensure that the standard _split() method works as advertised