diff --git a/src/AccessControl/AccessControl.txt b/src/AccessControl/AccessControl.txt
index ec127ed..e5b4389 100644
--- a/src/AccessControl/AccessControl.txt
+++ b/src/AccessControl/AccessControl.txt
@@ -205,7 +205,7 @@ Example:
 
     __ac_types__=(
 
-    ('Full Access', map(lambda x: x[0], __ac_permissions__)),
+    ('Full Access', tuple(map(lambda x: x[0], __ac_permissions__))),
     ('Change', ['Add Objects', 'Add Properties', 'Change Properties']),
 
     )
diff --git a/src/AccessControl/rolemanager.py b/src/AccessControl/rolemanager.py
index 152f9d4..b52a498 100644
--- a/src/AccessControl/rolemanager.py
+++ b/src/AccessControl/rolemanager.py
@@ -105,13 +105,13 @@ def permission_settings(self, permission=None):
             d={'name': name,
                'hashed_name': _string_hash(name),
                'acquire': isinstance(roles, list) and 'CHECKED' or '',
-               'roles': map(
+               'roles': tuple(map(
                    lambda ir, roles=roles, valid=valid, ip=ip:
                    {
                        'name': "permission_%srole_%s" % (_string_hash(permission_name), _string_hash(valid[ir])),
                        'checked': (valid[ir] in roles) and 'CHECKED' or '',
                        },
-                   indexes)
+                   indexes))
                }
             ip = ip + 1
             result.append(d)
@@ -243,12 +243,12 @@ def rolesOfPermission(self, permission):
             if name==permission:
                 p = Permission(name, value, self)
                 roles = p.getRoles()
-                return map(
+                return tuple(map(
                     lambda role, roles=roles:
                     {'name': role,
                      'selected': role in roles and 'SELECTED' or '',
                      },
-                    valid_roles)
+                    valid_roles))
 
         raise ValueError(
             "The permission <em>%s</em> is invalid." % escape(permission))
diff --git a/src/AccessControl/tainted.py b/src/AccessControl/tainted.py
index 290da5d..51e333f 100644
--- a/src/AccessControl/tainted.py
+++ b/src/AccessControl/tainted.py
@@ -19,8 +19,12 @@
 """
 
 from cgi import escape
+from functools import total_ordering
 
+import six
 
+
+@total_ordering
 class TaintedString:
 
     def __init__(self, value):
@@ -32,8 +36,15 @@ def __str__(self):
     def __repr__(self):
         return repr(self.quoted())
 
-    def __cmp__(self, o):
-        return cmp(self._value, o)
+    if six.PY2:
+        def __cmp__(self, o):
+            return cmp(self._value, o)  # NOQA
+
+    def __eq__(self, o):
+        return self._value == o
+
+    def __lt__(self, o):
+        return self._value < o
 
     def __hash__(self):
         return hash(self._value)
@@ -76,8 +87,9 @@ def __int__(self):
     def __float__(self):
         return float(self._value)
 
-    def __long__(self):
-        return long(self._value)
+    if six.PY2:
+        def __long__(self):
+            return long(self._value)  # NOQA
 
     def __getstate__(self):
         # If an object tries to store a TaintedString, it obviously wasn't
@@ -108,11 +120,11 @@ def replace(self, *args):
 
     def split(self, *args):
         r = self._value.split(*args)
-        return map(lambda v, c=self.__class__: '<' in v and c(v) or v, r)
+        return list(map(lambda v, c=self.__class__: '<' in v and c(v) or v, r))
 
     def splitlines(self, *args):
         r = self._value.splitlines(*args)
-        return map(lambda v, c=self.__class__: '<' in v and c(v) or v, r)
+        return list(map(lambda v, c=self.__class__: '<' in v and c(v) or v, r))
 
     def translate(self, *args):
         v = self._value.translate(*args)
diff --git a/src/AccessControl/tests/test_tainted.py b/src/AccessControl/tests/test_tainted.py
index d96541c..b650909 100644
--- a/src/AccessControl/tests/test_tainted.py
+++ b/src/AccessControl/tests/test_tainted.py
@@ -15,6 +15,8 @@
 
 import unittest
 
+import six
+
 
 class TestTaintedString(unittest.TestCase):
 
@@ -34,9 +36,9 @@ def testRepr(self):
         self.assertEquals(repr(self.tainted), repr(self.quoted))
 
     def testCmp(self):
-        self.assertEquals(cmp(self.tainted, self.unquoted), 0)
-        self.assertEquals(cmp(self.tainted, 'a'), -1)
-        self.assertEquals(cmp(self.tainted, '.'), 1)
+        self.assertTrue(self.tainted == self.unquoted)
+        self.assertTrue(self.tainted < 'a')
+        self.assertTrue(self.tainted > '.')
 
     def testHash(self):
         hash = {}
@@ -147,9 +149,11 @@ def testStringMethods(self):
                           unquoted.translate(transtable))
         self.assert_(isinstance(self._getClass()('<').translate(transtable),
                                 self._getClass()))
-        self.failIf(isinstance(self._getClass()('<').translate(transtable,
-                                                               '<'),
-                               self._getClass()))
+        if six.PY2:
+            # Translate no longer supports a second argument
+            self.failIf(isinstance(self._getClass()('<').translate(transtable,
+                                                                   '<'),
+                                   self._getClass()))
 
     def testQuoted(self):
         self.assertEquals(self.tainted.quoted(), self.quoted)