diff --git a/CHANGES.rst b/CHANGES.rst
index 0203e6a..aea7438 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -4,7 +4,12 @@ Changes
 4.1.1 (unreleased)
 ------------------
 
-- TBD
+- Fix `issue 23 <https://github.com/zopefoundation/zope.security/issues/23>`_:
+  iteration of ``collections.OrderedDict`` and its various views is
+  now allowed by default on all versions of Python.
+
+- As a further fix for issue 20, iteration of BTree itself is now
+  allowed by default.
 
 4.1.0 (2017-04-24)
 ------------------
diff --git a/src/zope/security/checker.py b/src/zope/security/checker.py
index 3187afc..344428c 100644
--- a/src/zope/security/checker.py
+++ b/src/zope/security/checker.py
@@ -770,6 +770,27 @@ def f(): #pragma NO COVER
     _default_checkers[type({}.iterkeys())] = _iteratorChecker
     _default_checkers[type({}.itervalues())] = _iteratorChecker
 
+def _fixup_dictlike(dict_type):
+    empty_dict = dict_type()
+    populated_dict = dict_type({1: 2})
+    for dictlike in (empty_dict, populated_dict):
+        for attr in ('__iter__', 'keys', 'items', 'values'):
+            obj = getattr(dictlike, attr)()
+            o_type = type(obj)
+            if o_type not in _default_checkers:
+                _default_checkers[o_type] = _iteratorChecker
+
+def _fixup_odict():
+    # OrderedDicts have three different implementations: Python 2 (pure
+    # python, returns generators and lists), Python <=3.4 (pure Python,
+    # uses view classes) and CPython 3.5+ (implemented in C). These should
+    # all be iterable.
+    from collections import OrderedDict
+    _fixup_dictlike(OrderedDict)
+
+_fixup_odict()
+del _fixup_odict
+
 try:
     import BTrees
 except ImportError: # pragma: no cover
@@ -794,20 +815,14 @@ def _fixup_btrees():
         for name in ('IF', 'II', 'IO', 'OI', 'OO'):
             for family_name in ('family32', 'family64'):
                 family = getattr(BTrees, family_name)
-                btree = getattr(family, name).BTree()
-
-                empty_type = type(btree.items())
-                if empty_type not in _default_checkers:
-                    _default_checkers[empty_type] = _iteratorChecker
-
-                btree[1] = 1
-                populated_type = type(btree.items())
-                if populated_type not in _default_checkers:
-                    _default_checkers[populated_type] = _iteratorChecker
+                btree = getattr(family, name).BTree
+                _fixup_dictlike(btree)
 
     _fixup_btrees()
     del _fixup_btrees
 
+del _fixup_dictlike
+
 def _clear():
     _checkers.clear()
     _checkers.update(_default_checkers)
diff --git a/src/zope/security/tests/test_checker.py b/src/zope/security/tests/test_checker.py
index ceda502..03a8883 100644
--- a/src/zope/security/tests/test_checker.py
+++ b/src/zope/security/tests/test_checker.py
@@ -391,34 +391,48 @@ def _check(*args):
         finally:
             _clear()
 
-    @_skip_if_no_btrees
-    def test_iteration_of_btree_items(self):
-        # iteration of BTree.items() is allowed by default.
+    def _check_iteration_of_dict_like(self, dict_like):
         from zope.security.proxy import Proxy
         from zope.security.checker import Checker
-        from zope.security.checker import CheckerPublic
-        import BTrees
+        from zope.security.checker import _default_checkers
+
+        checker = _default_checkers[dict]
+
+        proxy = Proxy(dict_like, checker)
+        # empty
+        self.assertEqual([], list(proxy.items()))
+        self.assertEqual([], list(proxy.keys()))
+        self.assertEqual([], list(proxy.values()))
+        self.assertEqual([], list(proxy))
 
-        checker = Checker({'items': CheckerPublic,
-                           'keys': CheckerPublic,
-                           'values': CheckerPublic})
+        # With an object
+        dict_like[1] = 2
+        self.assertEqual([(1, 2)], list(proxy.items()))
+        self.assertEqual([1], list(proxy.keys()))
+        self.assertEqual([1], list(proxy))
+        self.assertEqual([2], list(proxy.values()))
 
+
+    @_skip_if_no_btrees
+    def test_iteration_of_btree_items_keys_values(self):
+        # iteration of BTree.items() is allowed by default.
+        import BTrees
         for name in ('IF', 'II', 'IO', 'OI', 'OO'):
             for family_name in ('family32', 'family64'):
                 family = getattr(BTrees, family_name)
                 btree = getattr(family, name).BTree()
-                proxy = Proxy(btree, checker)
-                # empty
-                self.assertEqual([], list(proxy.items()))
-                self.assertEqual([], list(proxy.keys()))
-                self.assertEqual([], list(proxy.values()))
-
-                # With an object
-                btree[1] = 2
-                self.assertEqual([(1, 2)], list(proxy.items()))
-                self.assertEqual([1], list(proxy.keys()))
-                self.assertEqual([2], list(proxy.values()))
+                self._check_iteration_of_dict_like(btree)
+
+    def test_iteration_of_odict_items_keys_values(self):
+        # iteration of OrderedDict.items() is allowed by default.
+        from collections import OrderedDict
+
+        odict = OrderedDict()
+        self._check_iteration_of_dict_like(odict)
 
+    def test_iteration_of_dict_items_keys_values(self):
+        # iteration of regular dict is allowed by default
+        self._check_iteration_of_dict_like(dict())
 
 class CheckerPyTests(unittest.TestCase, CheckerTestsBase):