diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index bb0cfe7502f2aba..af5aadb69b80a0c 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -6156,6 +6156,8 @@ def clientSetUp(self):
         self.source_port = socket_helper.find_unused_port()
 
     def clientTearDown(self):
+        # TestCase cleanups run in the server thread and could close the
+        # socket while the client thread is still using it.
         if self.cli is not None:
             self.cli.close()
         self.cli = None
@@ -6169,7 +6171,6 @@ def _justAccept(self):
     def _testFamily(self):
         self.cli = socket.create_connection((HOST, self.port),
                             timeout=support.LOOPBACK_TIMEOUT)
-        self.addCleanup(self.cli.close)
         self.assertEqual(self.cli.family, 2)
 
     testSourceAddress = _justAccept
@@ -6177,7 +6178,6 @@ def _testSourceAddress(self):
         self.cli = socket.create_connection((HOST, self.port),
                             timeout=support.LOOPBACK_TIMEOUT,
                             source_address=('', self.source_port))
-        self.addCleanup(self.cli.close)
         self.assertEqual(self.cli.getsockname()[1], self.source_port)
         # The port number being used is sufficient to show that the bind()
         # call happened.
@@ -6189,7 +6189,6 @@ def _testTimeoutDefault(self):
         socket.setdefaulttimeout(42)
         try:
             self.cli = socket.create_connection((HOST, self.port))
-            self.addCleanup(self.cli.close)
         finally:
             socket.setdefaulttimeout(None)
         self.assertEqual(self.cli.gettimeout(), 42)
@@ -6201,7 +6200,6 @@ def _testTimeoutNone(self):
         socket.setdefaulttimeout(30)
         try:
             self.cli = socket.create_connection((HOST, self.port), timeout=None)
-            self.addCleanup(self.cli.close)
         finally:
             socket.setdefaulttimeout(None)
         self.assertEqual(self.cli.gettimeout(), None)
@@ -6214,7 +6212,6 @@ def _testTimeoutValueNamed(self):
     testTimeoutValueNonamed = _justAccept
     def _testTimeoutValueNonamed(self):
         self.cli = socket.create_connection((HOST, self.port), 30)
-        self.addCleanup(self.cli.close)
         self.assertEqual(self.cli.gettimeout(), 30)