diff --git a/Lib/random.py b/Lib/random.py
index 7210f62b100..2530c39ac76 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -258,6 +258,10 @@ class Random(_random.Random):
                 result[i] = pool[j]
                 pool[j] = pool[n-i-1]   # move non-selected item into vacancy
         else:
+            try:
+                n > 0 and (population[0], population[n//2], population[n-1])
+            except (TypeError, KeyError):   # handle sets and dictionaries
+                population = tuple(population)
             selected = {}
             for i in xrange(k):
                 j = _int(random() * n)
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index c9103e8f87b..fbd418457a6 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -86,6 +86,16 @@ class TestBasicOps(unittest.TestCase):
             else:
                 self.fail()
 
+    def test_sample_inputs(self):
+        # SF bug #801342 -- population can be any iterable defining __len__()
+        from sets import Set
+        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_gauss(self):
         # Ensure that the seed() method initializes all the hidden state.  In
         # particular, through 2.2.1 it failed to reset a piece of state used