diff --git a/Lib/test/test_re.py b/Lib/test/test_re.py
index 268d66d..86eda54 100644
--- a/Lib/test/test_re.py
+++ b/Lib/test/test_re.py
@@ -1,7 +1,10 @@
 from test.support import verbose, run_unittest
 import re
 from re import Scanner
-import sys, os, traceback
+import os
+import sys
+import string
+import traceback
 from weakref import proxy
 
 # Misc tests from Tim Peters' re.doc
@@ -411,31 +414,46 @@
         self.assertEqual(re.search("\s(b)", " b").group(1), "b")
         self.assertEqual(re.search("a\s", "a ").group(0), "a ")
 
-    def test_re_escape(self):
-        p=""
-        self.assertEqual(re.escape(p), p)
-        for i in range(0, 256):
-            p = p + chr(i)
-            self.assertEqual(re.match(re.escape(chr(i)), chr(i)) is not None,
-                             True)
-            self.assertEqual(re.match(re.escape(chr(i)), chr(i)).span(), (0,1))
+    def assertMatch(self, pattern, text, match=None, span=None,
+                    matcher=re.match):
+        if match is None and span is None:
+            # the pattern matches the whole text
+            match = text
+            span = (0, len(text))
+        elif match is None or span is None:
+            raise ValueError('If match is not None, span should be specified '
+                             '(and vice versa).')
+        m = matcher(pattern, text)
+        self.assertTrue(m)
+        self.assertEqual(m.group(), match)
+        self.assertEqual(m.span(), span)
 
-        pat=re.compile(re.escape(p))
-        self.assertEqual(pat.match(p) is not None, True)
-        self.assertEqual(pat.match(p).span(), (0,256))
+    def test_re_escape(self):
+        alnum_chars = string.ascii_letters + string.digits
+        p = ''.join(chr(i) for i in range(256))
+        for c in p:
+            if c in alnum_chars:
+                self.assertEqual(re.escape(c), c)
+            elif c == '\x00':
+                self.assertEqual(re.escape(c), '\\000')
+            else:
+                self.assertEqual(re.escape(c), '\\' + c)
+            self.assertMatch(re.escape(c), c)
+        self.assertMatch(re.escape(p), p)
 
     def test_re_escape_byte(self):
-        p=b""
-        self.assertEqual(re.escape(p), p)
-        for i in range(0, 256):
+        alnum_chars = (string.ascii_letters + string.digits).encode('ascii')
+        p = bytes(range(256))
+        for i in p:
             b = bytes([i])
-            p += b
-            self.assertEqual(re.match(re.escape(b), b) is not None, True)
-            self.assertEqual(re.match(re.escape(b), b).span(), (0,1))
-
-        pat=re.compile(re.escape(p))
-        self.assertEqual(pat.match(p) is not None, True)
-        self.assertEqual(pat.match(p).span(), (0,256))
+            if b in alnum_chars:
+                self.assertEqual(re.escape(b), b)
+            elif i == 0:
+                self.assertEqual(re.escape(b), b'\\000')
+            else:
+                self.assertEqual(re.escape(b), b'\\' + b)
+            self.assertMatch(re.escape(b), b)
+        self.assertMatch(re.escape(p), p)
 
     def pickle_test(self, pickle):
         oldpat = re.compile('a(?:b|(c|e){1,2}?|d)+?(.)')