diff --git a/Lib/test/test_multiprocessing.py b/Lib/test/test_multiprocessing.py
index 03629d1..59b3357 100644
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -1262,9 +1262,9 @@
 
     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))
@@ -1274,7 +1274,7 @@
         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 977a152..b74fa40 100644
--- a/Lib/test/test_smtplib.py
+++ b/Lib/test/test_smtplib.py
@@ -155,8 +155,10 @@
         self._threads = test_support.threading_setup()
         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)
         self.thread = threading.Thread(target=debugging_server, args=serv_args)
         self.thread.start()
@@ -392,8 +394,10 @@
         self._threads = test_support.threading_setup()
         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)
         self.thread = threading.Thread(target=debugging_server, args=serv_args)
         self.thread.start()