diff --git a/Lib/test/string_tests.py b/Lib/test/string_tests.py
index f2173a7b29c..9f092b97937 100644
--- a/Lib/test/string_tests.py
+++ b/Lib/test/string_tests.py
@@ -737,26 +737,27 @@ class MixinStrUserStringTest:
     # Additional tests that only work with
     # 8bit compatible object, i.e. str and UserString
 
-    def test_encoding_decoding(self):
-        codecs = [('rot13', 'uryyb jbeyq'),
-                  ('base64', 'aGVsbG8gd29ybGQ=\n'),
-                  ('hex', '68656c6c6f20776f726c64'),
-                  ('uu', 'begin 666 <data>\n+:&5L;&\\@=V]R;&0 \n \nend\n')]
-        for encoding, data in codecs:
-            self.checkequal(data, 'hello world', 'encode', encoding)
-            self.checkequal('hello world', data, 'decode', encoding)
-        # zlib is optional, so we make the test optional too...
-        try:
-            import zlib
-        except ImportError:
-            pass
-        else:
-            data = 'x\x9c\xcbH\xcd\xc9\xc9W(\xcf/\xcaI\x01\x00\x1a\x0b\x04]'
-            self.checkequal(data, 'hello world', 'encode', 'zlib')
-            self.checkequal('hello world', data, 'decode', 'zlib')
+    if test_support.have_unicode:
+        def test_encoding_decoding(self):
+            codecs = [('rot13', 'uryyb jbeyq'),
+                      ('base64', 'aGVsbG8gd29ybGQ=\n'),
+                      ('hex', '68656c6c6f20776f726c64'),
+                      ('uu', 'begin 666 <data>\n+:&5L;&\\@=V]R;&0 \n \nend\n')]
+            for encoding, data in codecs:
+                self.checkequal(data, 'hello world', 'encode', encoding)
+                self.checkequal('hello world', data, 'decode', encoding)
+            # zlib is optional, so we make the test optional too...
+            try:
+                import zlib
+            except ImportError:
+                pass
+            else:
+                data = 'x\x9c\xcbH\xcd\xc9\xc9W(\xcf/\xcaI\x01\x00\x1a\x0b\x04]'
+                self.checkequal(data, 'hello world', 'encode', 'zlib')
+                self.checkequal('hello world', data, 'decode', 'zlib')
 
-        self.checkraises(TypeError, 'xyz', 'decode', 42)
-        self.checkraises(TypeError, 'xyz', 'encode', 42)
+            self.checkraises(TypeError, 'xyz', 'decode', 42)
+            self.checkraises(TypeError, 'xyz', 'encode', 42)
 
 
 class MixinStrUnicodeTest: