diff --git a/Lib/test/test_collections.py b/Lib/test/test_collections.py
index 13ae9bf..ddf8398 100644
--- a/Lib/test/test_collections.py
+++ b/Lib/test/test_collections.py
@@ -2,6 +2,8 @@
 from test import test_support
 from collections import namedtuple, Counter, Mapping
 import pickle, cPickle, copy
+from random import randrange
+import operator
 from collections import Hashable, Iterable, Iterator
 from collections import Sized, Container, Callable
 from collections import Set, MutableSet
@@ -350,6 +352,8 @@
 
     def test_basics(self):
         c = Counter('abcaba')
+        self.assertEqual(c, Counter({'a':3 , 'b': 2, 'c': 1}))
+        self.assertEqual(c, Counter(a=3, b=2, c=1))
         self.assert_(isinstance(c, dict))
         self.assert_(isinstance(c, Mapping))
         self.assert_(issubclass(Counter, dict))
@@ -379,6 +383,7 @@
         c['a'] += 1         # increment an existing value
         c['b'] -= 2         # sub existing value to zero
         del c['c']          # remove an entry
+        del c['c']          # make sure that del doesn't raise KeyError
         c['d'] -= 2         # sub from a missing value
         c['e'] = -5         # directly assign a missing value
         c['f'] += 4         # add to a missing value
@@ -394,7 +399,8 @@
         self.assertEqual(repr(c), 'Counter()')
         self.assertRaises(NotImplementedError, Counter.fromkeys, 'abc')
         self.assertRaises(TypeError, hash, c)
-        c.update(dict(a=5, b=3, c=1))
+        c.update(dict(a=5, b=3))
+        c.update(c=1)
         c.update(Counter('a' * 50 + 'b' * 30))
         c.update()          # test case with no args
         c.__init__('a' * 500 + 'b' * 300)
@@ -442,6 +448,43 @@
         self.assertEqual(dict(Counter(s)), dict(Counter(s).items()))
         self.assertEqual(set(Counter(s)), set(s))
 
+    def test_multiset_operations(self):
+        # Verify that adding a zero counter will strip zeros and negatives
+        c = Counter(a=10, b=-2, c=0) + Counter()
+        self.assertEqual(dict(c), dict(a=10))
+
+        elements = 'abcd'
+        for i in range(1000):
+            # test random pairs of multisets
+            p = Counter(dict((elem, randrange(-2,4)) for elem in elements))
+            q = Counter(dict((elem, randrange(-2,4)) for elem in elements))
+            for counterop, numberop, defneg in [
+                (Counter.__add__, lambda x, y: x+y if x+y>0 else 0, True),
+                (Counter.__sub__, lambda x, y: x-y if x-y>0 else 0, False),
+                (Counter.__or__, max, False),
+                (Counter.__and__, min, False),
+            ]:
+                result = counterop(p, q)
+                for x in elements:
+                    # all except __add__ are undefined for negative inputs
+                    if defneg or (p[x] >= 0 and q[x] >= 0):
+                        self.assertEqual(numberop(p[x], q[x]), result[x])
+                # verify that results exclude non-positive counts
+                self.assert_(x>0 for x in result.values())
+
+        elements = 'abcdef'
+        for i in range(100):
+            # verify that random multisets with no repeats are exactly like sets
+            p = Counter(dict((elem, randrange(0, 2)) for elem in elements))
+            q = Counter(dict((elem, randrange(0, 2)) for elem in elements))
+            for counterop, setop in [
+                (Counter.__sub__, set.__sub__),
+                (Counter.__or__, set.__or__),
+                (Counter.__and__, set.__and__),
+            ]:
+                counter_result = counterop(p, q)
+                set_result = setop(set(p.elements()), set(q.elements()))
+                self.assertEqual(counter_result, dict.fromkeys(set_result, 1))
 
 import doctest, collections