diff --git a/Lib/concurrent/futures/process.py b/Lib/concurrent/futures/process.py
index 7c22a62..9b2e0f3 100644
--- a/Lib/concurrent/futures/process.py
+++ b/Lib/concurrent/futures/process.py
@@ -205,12 +205,12 @@
         nb_children_alive = sum(p.is_alive() for p in processes.values())
         for i in range(0, nb_children_alive):
             call_queue.put_nowait(None)
+        # Release the queue's resources as soon as possible.
+        call_queue.close()
         # If .join() is not called on the created processes then
         # some multiprocessing.Queue methods may deadlock on Mac OS X.
         for p in processes.values():
             p.join()
-        # Release resources held by the queue
-        call_queue.close()
 
     while True:
         _add_call_item_to_queue(pending_work_items,
@@ -241,8 +241,7 @@
             # locks may be in a dirty state and block forever.
             for p in processes.values():
                 p.terminate()
-            for p in processes.values():
-                p.join()
+            shutdown_worker()
             return
         if isinstance(result_item, int):
             # Clean shutdown of a worker using its PID
@@ -337,6 +336,10 @@
         # because futures in the call queue cannot be cancelled.
         self._call_queue = multiprocessing.Queue(self._max_workers +
                                                  EXTRA_QUEUED_CALLS)
+        # Killed worker processes can produce spurious "broken pipe"
+        # tracebacks in the queue's own worker thread. But we detect killed
+        # processes anyway, so silence the tracebacks.
+        self._call_queue._ignore_epipe = True
         self._result_queue = SimpleQueue()
         self._work_ids = queue.Queue()
         self._queue_management_thread = None