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  -------------------