diff --git a/Lib/test/test_smtplib.py b/Lib/test/test_smtplib.py
index d36ab0e..3a9de5b 100644
--- a/Lib/test/test_smtplib.py
+++ b/Lib/test/test_smtplib.py
@@ -163,8 +163,10 @@
         self._threads = support.threading_setup()
         self.serv_evt = threading.Event()
         self.client_evt = threading.Event()
-        self.port = 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()
@@ -400,8 +402,10 @@
         self._threads = support.threading_setup()
         self.serv_evt = threading.Event()
         self.client_evt = threading.Event()
-        self.port = 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()