diff --git a/Lib/test/test_multiprocessing.py b/Lib/test/test_multiprocessing.py
index f901a05..c5aeb14 100644
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -1221,9 +1221,9 @@
 
     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))
@@ -1233,7 +1233,7 @@
         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 fff319d..727ef83 100644
--- a/Lib/test/test_smtplib.py
+++ b/Lib/test/test_smtplib.py
@@ -152,8 +152,10 @@
 
         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)
         threading.Thread(target=debugging_server, args=serv_args).start()
 
@@ -379,8 +381,10 @@
     def setUp(self):
         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)
         threading.Thread(target=debugging_server, args=serv_args).start()
 
diff --git a/Misc/NEWS b/Misc/NEWS
index bfc6772..5414512 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -137,6 +137,9 @@
 Tests
 -----
 
+- Issue #8576: Remove use of find_unused_port() in test_smtplib and
+  test_multiprocessing.  Patch by Paul Moore.
+
 - Issue #8531: Skip test_ascii_formatd if ctypes module is missing
 
 - Issue #3864: Skip three test_signal tests on freebsd6 because they fail