diff --git a/Lib/test/test_queue.py b/Lib/test/test_queue.py
index 0bd395ad379..b55dd01f22a 100644
--- a/Lib/test/test_queue.py
+++ b/Lib/test/test_queue.py
@@ -18,26 +18,62 @@ class _TriggerThread(threading.Thread):
         threading.Thread.__init__(self)
 
     def run(self):
-        time.sleep(.1)
+        # The sleep isn't necessary, but is intended to give the blocking
+        # function in the main thread a chance at actually blocking before
+        # we unclog it.  But if the sleep is longer than the timeout-based
+        # tests wait in their blocking functions, those tests will fail.
+        # So we give them much longer timeout values compared to the
+        # sleep here (I aimed at 10 seconds for blocking functions --
+        # they should never actually wait that long - they should make
+        # progress as soon as we call self.fn()).
+        time.sleep(0.1)
         self.startedEvent.set()
         self.fn(*self.args)
 
-# Execute a function that blocks, and in a seperate thread, a function that
+# Execute a function that blocks, and in a separate thread, a function that
 # triggers the release.  Returns the result of the blocking function.
+# Caution:  block_func must guarantee to block until trigger_func is
+# called, and trigger_func must guarantee to change queue state so that
+# block_func can make enough progress to return.  In particular, a
+# block_func that just raises an exception regardless of whether trigger_func
+# is called will lead to timing-dependent sporadic failures, and one of
+# those went rarely seen but undiagnosed for years.  Now block_func
+# must be unexceptional.  If block_func is supposed to raise an exception,
+# call _doExceptionalBlockingTest() instead.
 def _doBlockingTest(block_func, block_args, trigger_func, trigger_args):
     t = _TriggerThread(trigger_func, trigger_args)
     t.start()
+    result = block_func(*block_args)
+    # If block_func returned before our thread made the call, we failed!
+    if not t.startedEvent.isSet():
+        raise TestFailed("blocking function '%r' appeared not to block" %
+                         block_func)
+    t.join(10) # make sure the thread terminates
+    if t.isAlive():
+        raise TestFailed("trigger function '%r' appeared to not return" %
+                         trigger_func)
+    return result
+
+# Call this instead if block_func is supposed to raise an exception.
+def _doExceptionalBlockingTest(block_func, block_args, trigger_func,
+                               trigger_args, expected_exception_class):
+    t = _TriggerThread(trigger_func, trigger_args)
+    t.start()
     try:
-        return block_func(*block_args)
+        try:
+            block_func(*block_args)
+        except expected_exception_class:
+            raise
+        else:
+            raise TestFailed("expected exception of kind %r" %
+                             expected_exception_class)
     finally:
-        # If we unblocked before our thread made the call, we failed!
-        if not t.startedEvent.isSet():
-            raise TestFailed("blocking function '%r' appeared not to block" %
-                             block_func)
-        t.join(1) # make sure the thread terminates
+        t.join(10) # make sure the thread terminates
         if t.isAlive():
             raise TestFailed("trigger function '%r' appeared to not return" %
                              trigger_func)
+        if not t.startedEvent.isSet():
+            raise TestFailed("trigger thread ended but event never set")
 
 # A Queue subclass that can provoke failure at a moment's notice :)
 class FailingQueueException(Exception):
@@ -92,7 +128,8 @@ def FailingQueueTest(q):
     # Test a failing timeout put
     q.fail_next_put = True
     try:
-        _doBlockingTest(q.put, ("full", True, 0.2), q.get, ())
+        _doExceptionalBlockingTest(q.put, ("full", True, 10), q.get, (),
+                                   FailingQueueException)
         raise TestFailed("The queue didn't fail when it should have")
     except FailingQueueException:
         pass
@@ -129,7 +166,8 @@ def FailingQueueTest(q):
     verify(q.empty(), "Queue should be empty")
     q.fail_next_get = True
     try:
-        _doBlockingTest( q.get, (), q.put, ('empty',))
+        _doExceptionalBlockingTest(q.get, (), q.put, ('empty',),
+                                   FailingQueueException)
         raise TestFailed("The queue didn't fail when it should have")
     except FailingQueueException:
         pass
@@ -148,6 +186,7 @@ def SimpleQueueTest(q):
            "Didn't seem to queue the correct data!")
     for i in range(QUEUE_SIZE-1):
         q.put(i)
+        verify(not q.empty(), "Queue should not be empty")
     verify(not q.full(), "Queue should not be full")
     q.put("last")
     verify(q.full(), "Queue should be full")
@@ -157,13 +196,13 @@ def SimpleQueueTest(q):
     except Queue.Full:
         pass
     try:
-        q.put("full", timeout=0.1)
+        q.put("full", timeout=0.01)
         raise TestFailed("Didn't appear to time-out with a full queue")
     except Queue.Full:
         pass
     # Test a blocking put
     _doBlockingTest(q.put, ("full",), q.get, ())
-    _doBlockingTest(q.put, ("full", True, 0.2), q.get, ())
+    _doBlockingTest(q.put, ("full", True, 10), q.get, ())
     # Empty it
     for i in range(QUEUE_SIZE):
         q.get()
@@ -174,13 +213,13 @@ def SimpleQueueTest(q):
     except Queue.Empty:
         pass
     try:
-        q.get(timeout=0.1)
+        q.get(timeout=0.01)
         raise TestFailed("Didn't appear to time-out with an empty queue")
     except Queue.Empty:
         pass
     # Test a blocking get
     _doBlockingTest(q.get, (), q.put, ('empty',))
-    _doBlockingTest(q.get, (True, 0.2), q.put, ('empty',))
+    _doBlockingTest(q.get, (True, 10), q.put, ('empty',))
 
 def test():
     q = Queue.Queue(QUEUE_SIZE)