diff --git a/Lib/test/test_multiprocessing.py b/Lib/test/test_multiprocessing.py
index 4bd877c..2c1da0f 100644
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -1205,9 +1205,9 @@
 
     def test_rapid_restart(self):
         authkey = os.urandom(32)
-        port = test_support.find_unused_port()
         manager = QueueManager(
-            address=('localhost', port), authkey=authkey, serializer=SERIALIZER)
+            address=('localhost', 0), authkey=authkey, serializer=SERIALIZER)
+        addr = manager.get_server().address
         manager.start()
 
         p = self.Process(target=self._putter, args=(manager.address, authkey))
@@ -1217,7 +1217,7 @@
         del queue
         manager.shutdown()
         manager = QueueManager(
-            address=('localhost', port), authkey=authkey, serializer=SERIALIZER)
+            address=addr, authkey=authkey, serializer=SERIALIZER)
         manager.start()
         manager.shutdown()
 
diff --git a/Lib/test/test_smtplib.py b/Lib/test/test_smtplib.py
index 9a498d2..644cbf7 100644
--- a/Lib/test/test_smtplib.py
+++ b/Lib/test/test_smtplib.py
@@ -144,8 +144,10 @@
 
         self.serv_evt = threading.Event()
         self.client_evt = threading.Event()
-        self.port = test_support.find_unused_port()
-        self.serv = smtpd.DebuggingServer((HOST, self.port), ('nowhere', -1))
+        # Pick a random unused port by passing 0 for the port number
+        self.serv = smtpd.DebuggingServer((HOST, 0), ('nowhere', -1))
+        # Keep a note of what port was assigned
+        self.port = self.serv.socket.getsockname()[1]
         serv_args = (self.serv, self.serv_evt, self.client_evt)
         threading.Thread(target=debugging_server, args=serv_args).start()
 
@@ -371,8 +373,10 @@
     def setUp(self):
         self.serv_evt = threading.Event()
         self.client_evt = threading.Event()
-        self.port = test_support.find_unused_port()
-        self.serv = SimSMTPServer((HOST, self.port), ('nowhere', -1))
+        # Pick a random unused port by passing 0 for the port number
+        self.serv = SimSMTPServer((HOST, 0), ('nowhere', -1))
+        # Keep a note of what port was assigned
+        self.port = self.serv.socket.getsockname()[1]
         serv_args = (self.serv, self.serv_evt, self.client_evt)
         threading.Thread(target=debugging_server, args=serv_args).start()