diff -r fae92299eb68 Lib/concurrent/futures/_base.py
--- a/Lib/concurrent/futures/_base.py	Sat Jan 25 13:27:53 2014 -0500
+++ b/Lib/concurrent/futures/_base.py	Sat Jan 25 16:36:48 2014 -0500
@@ -249,12 +249,14 @@
         A named 2-tuple of sets. The first set, named 'done', contains the
         futures that completed (is finished or cancelled) before the wait
         completed. The second set, named 'not_done', contains uncompleted
-        futures.
+        futures. If any given Futures are duplicated, they will be returned 
+        once.
     """
+    fs = set(fs)
     with _AcquireFutures(fs):
         done = set(f for f in fs
                    if f._state in [CANCELLED_AND_NOTIFIED, FINISHED])
-        not_done = set(fs) - done
+        not_done = fs - done
 
         if (return_when == FIRST_COMPLETED) and done:
             return DoneAndNotDoneFutures(done, not_done)
diff -r fae92299eb68 Lib/test/test_concurrent_futures.py
--- a/Lib/test/test_concurrent_futures.py	Sat Jan 25 13:27:53 2014 -0500
+++ b/Lib/test/test_concurrent_futures.py	Sat Jan 25 16:36:48 2014 -0500
@@ -290,6 +290,21 @@
                               future1]), finished)
         self.assertEqual(set([future2]), pending)
 
+    def test_duplicate_futures(self):
+        # Issue #20369: wait() on duplicate finished futures should not trigger 
+        # waiters to be installed.
+        future1 = self.executor.submit(mul, 6, 7)
+        time.sleep(1)
+        self.assertEqual(future1._state, FINISHED, "Precondition not valid for test")
+        start = time.time()
+        done, notdone = futures.wait([future1,future1], 
+            return_when=futures.ALL_COMPLETED,
+            timeout=2)
+        end = time.time()
+        self.assertEqual( set([future1]), done)
+        self.assertEqual( len(notdone), 0)
+        self.assertLess(end-start, 2, "Wait timed out on finished duplicated futures")
+
 
 class ThreadPoolWaitTests(ThreadPoolMixin, WaitTests, unittest.TestCase):