diff --git a/Lib/test/test_imaplib.py b/Lib/test/test_imaplib.py
--- a/Lib/test/test_imaplib.py
+++ b/Lib/test/test_imaplib.py
@@ -172,6 +172,119 @@
         self._send_tagged(tag, 'OK', 'LOGIN completed')
 
 
+class NewIMAPTests(unittest.TestCase):
+    _client = None
+
+    def _setup(self, imap_server, connect=True):
+        """
+        Setups imap_server (which should inherit SimpleIMAPHandler) for tests.
+        Returns (client, server).
+        """
+        class TestTCPServer(socketserver.TCPServer):
+            def handle_error(self, request, client_address):
+                """
+                End request and raise the error if one occurs.
+                """
+                self.close_request(request)
+                self.server_close()
+                raise
+
+        self.addCleanup(self._cleanup)
+        self._server = TestTCPServer((support.HOST, 0), imap_server)
+        self._thread = threading.Thread(
+            name=self._server.__class__.__name__,
+            target=self._server.serve_forever,
+            # Short poll interval to make the test finish quickly.
+            # Time between requests is short enough that we won't wake
+            # up spuriously too many times.
+            kwargs={'poll_interval': 0.01})
+        self._thread.daemon = True  # In case this function raises.
+        self._thread.start()
+
+        if connect:
+            self._client = imaplib.IMAP4(*self._server.server_address)
+
+        return self._client, self._server
+
+    def _cleanup(self):
+        """
+        Cleans up the test server. This method should not be called manually,
+        it's being add to cleanup queue in the _setup method already.
+        """
+        # if logout was called already we'd raise an exception trying to
+        # shutdown the client once again
+        if self._client is not None and self._client.state != 'LOGOUT':
+            self._client.shutdown()
+        # cleanup the server
+        self._server.shutdown()
+        self._server.server_close()
+        self._thread.join()
+
+    def test_issue5949(self):
+        class EOFHandler(socketserver.StreamRequestHandler):
+            def handle(self):
+                # EOF without sending a complete welcome message.
+                self.wfile.write(b'* OK')
+        _, server = self._setup(EOFHandler, connect=False)
+        self.assertRaises(imaplib.IMAP4.abort, imaplib.IMAP4, *server.server_address)
+
+    def test_line_termination(self):
+        class BadNewlineHandler(SimpleIMAPHandler):
+            def cmd_CAPABILITY(self, tag, args):
+                self._send(b'* CAPABILITY IMAP4rev1 AUTH\n')
+                self._send_tagged(tag, 'OK', 'CAPABILITY completed')
+        _, server = self._setup(BadNewlineHandler, connect=False)
+        self.assertRaises(imaplib.IMAP4.abort, imaplib.IMAP4, *server.server_address)
+
+    def test_enable_raises_error_if_not_AUTH(self):
+        class EnableHandler(SimpleIMAPHandler):
+            capabilities = 'AUTH ENABLE UTF8=ACCEPT'
+        client, _ = self._setup(EnableHandler)
+        self.assertFalse(client.utf8_enabled)
+        self.assertRaisesRegex(imaplib.IMAP4.error, 'command ENABLE illegal in state NONAUTH', client.enable, 'foo')
+        self.assertFalse(client.utf8_enabled)
+
+    def test_enable_raises_error_if_no_capability(self):
+        client, _ = self._setup(SimpleIMAPHandler)
+        self.assertRaisesRegex(imaplib.IMAP4.error, 'Server does not support ENABLE', client.enable, 'foo')
+
+    def test_enable_UTF8_raises_error_if_not_supported(self):
+        client, _ = self._setup(SimpleIMAPHandler)
+        typ, data = client.login('user', 'pass')
+        self.assertEqual(typ, 'OK')
+        self.assertRaisesRegex(imaplib.IMAP4.error, 'Server does not support ENABLE', client.enable, 'UTF8=ACCEPT')
+
+    # command tests
+
+    def test_login(self):
+        client, _ = self._setup(SimpleIMAPHandler)
+        typ, data = client.login('user', 'pass')
+        self.assertEqual(typ, 'OK')
+        self.assertEqual(data[0], b'LOGIN completed')
+        self.assertEqual(client.state, 'AUTH')
+
+    def test_logout(self):
+        client, _ = self._setup(SimpleIMAPHandler)
+        typ, data = client.login('user', 'pass')
+        self.assertEqual(typ, 'OK')
+        self.assertEqual(data[0], b'LOGIN completed')
+        typ, data = client.logout()
+        self.assertEqual(typ, 'BYE')
+        self.assertEqual(data[0], b'IMAP4ref1 Server logging out')
+        self.assertEqual(client.state, 'LOGOUT')
+
+    def test_lsub(self):
+        class LsubCmd(SimpleIMAPHandler):
+            def cmd_LSUB(self, tag, args):
+                self._send_textline('* LSUB () "." directoryA')
+                return self._send_tagged(tag, 'OK', 'LSUB completed')
+        client, _ = self._setup(LsubCmd)
+        client.login('user', 'pass')
+        typ, data = client.lsub()
+        self.assertEqual(typ, 'OK')
+        self.assertEqual(data[0], b'() "." directoryA')
+
+
 class ThreadedNetworkedTests(unittest.TestCase):
     server_class = socketserver.TCPServer
     imap_class = imaplib.IMAP4