diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
@@ -1889,7 +1889,11 @@ def wrap_conn(self):
                    # XXX Various errors can have happened here, for example
                    # a mismatching protocol version, an invalid certificate,
                    # or a low-level bug. This should be made more discriminating.
-                    self.server.conn_errors.append(e)
                    if self.server.chatty:
                        handle_error("\n server:  bad connection attempt from " + repr(self.addr) + ":\n")
                    self.running = False
@@ -3097,7 +3101,7 @@ def test_default_ciphers(self):
                with context.wrap_socket(socket.socket()) as s:
                    with self.assertRaises(OSError):
                        s.connect((HOST, server.port))
-            self.assertIn("no shared cipher", str(server.conn_errors[0]))

        def test_version_basic(self):
            """