diff --git a/Lib/test/test_dict.py b/Lib/test/test_dict.py
index c016681cc91..d81ecf59c49 100644
--- a/Lib/test/test_dict.py
+++ b/Lib/test/test_dict.py
@@ -398,6 +398,66 @@ class DictTest(unittest.TestCase):
         else:
             self.fail("< didn't raise Exc")
 
+    def test_keys_contained(self):
+        # Test rich comparisons against dict key views, which should behave the
+        # same as sets.
+        empty = dict()
+        empty2 = dict()
+        smaller = {1:1, 2:2}
+        larger = {1:1, 2:2, 3:3}
+        larger2 = {1:1, 2:2, 3:3}
+        larger3 = {4:1, 2:2, 3:3}
+
+        self.assertTrue(smaller.keys() <  larger.keys())
+        self.assertTrue(smaller.keys() <= larger.keys())
+        self.assertTrue(larger.keys() >  smaller.keys())
+        self.assertTrue(larger.keys() >= smaller.keys())
+
+        self.assertFalse(smaller.keys() >= larger.keys())
+        self.assertFalse(smaller.keys() >  larger.keys())
+        self.assertFalse(larger.keys()  <= smaller.keys())
+        self.assertFalse(larger.keys()  <  smaller.keys())
+
+        self.assertFalse(smaller.keys() <  larger3.keys())
+        self.assertFalse(smaller.keys() <= larger3.keys())
+        self.assertFalse(larger3.keys() >  smaller.keys())
+        self.assertFalse(larger3.keys() >= smaller.keys())
+
+        # Inequality strictness
+        self.assertTrue(larger2.keys() >= larger.keys())
+        self.assertTrue(larger2.keys() <= larger.keys())
+        self.assertFalse(larger2.keys() > larger.keys())
+        self.assertFalse(larger2.keys() < larger.keys())
+
+        self.assertTrue(larger.keys() == larger2.keys())
+        self.assertTrue(smaller.keys() != larger.keys())
+
+        # There is an optimization on the zero-element case.
+        self.assertTrue(empty.keys() == empty2.keys())
+        self.assertFalse(empty.keys() != empty2.keys())
+        self.assertFalse(empty.keys() == smaller.keys())
+        self.assertTrue(empty.keys() != smaller.keys())
+
+        # With the same size, an elementwise compare happens
+        self.assertTrue(larger.keys() != larger3.keys())
+        self.assertFalse(larger.keys() == larger3.keys())
+
+        # XXX the same tests for .items()
+
+    def test_errors_in_view_containment_check(self):
+        class C:
+            def __eq__(self, other):
+                raise RuntimeError
+        d1 = {1: C()}
+        d2 = {1: C()}
+        self.assertRaises(RuntimeError, lambda: d1.items() == d2.items())
+        self.assertRaises(RuntimeError, lambda: d1.items() != d2.items())
+        self.assertRaises(RuntimeError, lambda: d1.items() <= d2.items())
+        self.assertRaises(RuntimeError, lambda: d1.items() >= d2.items())
+        d3 = {1: C(), 2: C()}
+        self.assertRaises(RuntimeError, lambda: d2.items() < d3.items())
+        self.assertRaises(RuntimeError, lambda: d3.items() > d2.items())
+
     def test_missing(self):
         # Make sure dict doesn't have a __missing__ method
         self.assertEqual(hasattr(dict, "__missing__"), False)
diff --git a/Objects/dictobject.c b/Objects/dictobject.c
index a483b6cb4d8..9ef1fcc340f 100644
--- a/Objects/dictobject.c
+++ b/Objects/dictobject.c
@@ -2371,6 +2371,8 @@ PyTypeObject PyDictValues_Type;
 # define PyDictViewSet_Check(obj) \
 	(PyDictKeys_Check(obj) || PyDictItems_Check(obj))
 
+/* Return 1 if self is a subset of other, iterating over self;
+   0 if not; -1 if an error occurred. */
 static int
 all_contained_in(PyObject *self, PyObject *other)
 {
@@ -2398,41 +2400,63 @@ all_contained_in(PyObject *self, PyObject *other)
 static PyObject *
 dictview_richcompare(PyObject *self, PyObject *other, int op)
 {
+	Py_ssize_t len_self, len_other;
+	int ok;
+	PyObject *result;
+
 	assert(self != NULL);
 	assert(PyDictViewSet_Check(self));
 	assert(other != NULL);
-	if ((op == Py_EQ || op == Py_NE) &&
-	    (PyAnySet_Check(other) || PyDictViewSet_Check(other)))
-	{
-		Py_ssize_t len_self, len_other;
-		int ok;
-		PyObject *result;
 
-		len_self = PyObject_Size(self);
-		if (len_self < 0)
-			return NULL;
-		len_other = PyObject_Size(other);
-		if (len_other < 0)
-			return NULL;
-		if (len_self != len_other)
-			ok = 0;
-		else if (len_self == 0)
-			ok = 1;
-		else
-			ok = all_contained_in(self, other);
-		if (ok < 0)
-			return NULL;
-		if (ok == (op == Py_EQ))
-			result = Py_True;
-		else
-			result = Py_False;
-		Py_INCREF(result);
-		return result;
-	}
-	else {
+	if (!PyAnySet_Check(other) && !PyDictViewSet_Check(other)) {
 		Py_INCREF(Py_NotImplemented);
 		return Py_NotImplemented;
 	}
+
+	len_self = PyObject_Size(self);
+	if (len_self < 0)
+		return NULL;
+	len_other = PyObject_Size(other);
+	if (len_other < 0)
+		return NULL;
+
+	ok = 0;
+	switch(op) {
+
+	case Py_NE:
+	case Py_EQ:
+		if (len_self == len_other)
+			ok = all_contained_in(self, other);
+		if (op == Py_NE && ok >= 0)
+			ok = !ok;
+		break;
+
+	case Py_LT:
+		if (len_self < len_other)
+			ok = all_contained_in(self, other);
+		break;
+
+	  case Py_LE:
+		  if (len_self <= len_other)
+			  ok = all_contained_in(self, other);
+		  break;
+
+	case Py_GT:
+		if (len_self > len_other)
+			ok = all_contained_in(other, self);
+		break;
+
+	case Py_GE:
+		if (len_self >= len_other)
+			ok = all_contained_in(other, self);
+		break;
+
+	}
+	if (ok < 0)
+		return NULL;
+	result = ok ? Py_True : Py_False;
+	Py_INCREF(result);
+	return result;
 }
 
 /*** dict_keys ***/