diff --git a/Lib/random.py b/Lib/random.py
index 943fa51..465f477 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -285,6 +285,15 @@
         large population:   sample(xrange(10000000), 60)
         """
 
+        # XXX Although the documentation says `population` is "a sequence",
+        # XXX attempts are made to cater to any iterable with a __len__
+        # XXX method.  This has had mixed success.  Examples from both
+        # XXX sides:  sets work fine, and should become officially supported;
+        # XXX dicts are much harder, and have failed in various subtle
+        # XXX ways across attempts.  Support for mapping types should probably
+        # XXX be dropped (and users should pass mapping.keys() or .values()
+        # XXX explicitly).
+
         # Sampling without replacement entails tracking either potential
         # selections (the pool) in a list or previous selections in a set.
 
@@ -304,7 +313,9 @@
         setsize = 21        # size of a small set minus size of an empty list
         if k > 5:
             setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets
-        if n <= setsize:    # is an n-length list smaller than a k-length set
+        if n <= setsize or hasattr(population, "keys"):
+            # An n-length list is smaller than a k-length set, or this is a
+            # mapping type so the other algorithm wouldn't work.
             pool = list(population)
             for i in xrange(k):         # invariant:  non-selected at [0,n-i)
                 j = _int(random() * (n-i))
@@ -320,10 +331,10 @@
                         j = _int(random() * n)
                     selected_add(j)
                     result[i] = population[j]
-            except (TypeError, KeyError):   # handle sets and dictionaries
+            except (TypeError, KeyError):   # handle (at least) sets
                 if isinstance(population, list):
                     raise
-                return self.sample(list(population), k)
+                return self.sample(tuple(population), k)
         return result
 
 ## -------------------- real-valued distributions  -------------------
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index c9431b3..bba4c7c 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -93,12 +93,28 @@
         self.gen.sample(set(range(20)), 2)
         self.gen.sample(range(20), 2)
         self.gen.sample(xrange(20), 2)
-        self.gen.sample(dict.fromkeys('abcdefghijklmnopqrst'), 2)
         self.gen.sample(str('abcdefghijklmnopqrst'), 2)
         self.gen.sample(tuple('abcdefghijklmnopqrst'), 2)
+
+    def test_sample_on_dicts(self):
+        self.gen.sample(dict.fromkeys('abcdefghijklmnopqrst'), 2)
+
         # SF bug #1460340 -- random.sample can raise KeyError
         a = dict.fromkeys(range(10)+range(10,100,2)+range(100,110))
-        self.gen.sample(a,3)
+        self.gen.sample(a, 3)
+
+        # A followup to bug #1460340:  sampling from a dict could return
+        # a subset of its keys or of its values, depending on the size of
+        # the subset requested.
+        N = 30
+        d = dict((i, complex(i, i)) for i in xrange(N))
+        for k in xrange(N+1):
+            samp = self.gen.sample(d, k)
+            # Verify that we got ints back (keys); the values are complex.
+            for x in samp:
+                self.assert_(type(x) is int)
+        samp.sort()
+        self.assertEqual(samp, range(N))
 
     def test_gauss(self):
         # Ensure that the seed() method initializes all the hidden state.  In
diff --git a/Misc/NEWS b/Misc/NEWS
index ea5095f..974712a 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -489,6 +489,11 @@
 Library
 -------
 
+- Bug #1460340: ``random.sample(dict)`` failed in various ways.  Dicts
+  aren't officially supported here, and trying to use them will probably
+  raise an exception some day.  But dicts have been allowed, and "mostly
+  worked", so support for them won't go away without warning.
+
 - Bug #1445068: getpass.getpass() can now be given an explicit stream
   argument to specify where to write the prompt.