diff --git a/src/websockets/client.py b/src/websockets/client.py
index 8d826fea..df8e5342 100644
--- a/src/websockets/client.py
+++ b/src/websockets/client.py
@@ -336,6 +336,8 @@ def parse(self) -> Generator[None, None, None]:
             except InvalidHandshake as exc:
                 response._exception = exc
                 self.handshake_exc = exc
+                self.parser = self.discard()
+                next(self.parser)  # start coroutine
             else:
                 assert self.state is CONNECTING
                 self.state = OPEN
diff --git a/src/websockets/connection.py b/src/websockets/connection.py
index 967bd8fa..db8b5369 100644
--- a/src/websockets/connection.py
+++ b/src/websockets/connection.py
@@ -498,7 +498,7 @@ def close_expected(self) -> bool:
         #   applies, except on EOFError where we don't send a close frame
         #   because we already received the TCP close, so we don't expect it.
         # We already got a TCP Close if and only if the state is CLOSED.
-        return self.state is CLOSING
+        return self.state is CLOSING or self.handshake_exc is not None
 
     # Private methods for receiving data.
 
diff --git a/src/websockets/server.py b/src/websockets/server.py
index 214417ad..5dad50b6 100644
--- a/src/websockets/server.py
+++ b/src/websockets/server.py
@@ -13,6 +13,7 @@
     InvalidHeader,
     InvalidHeaderValue,
     InvalidOrigin,
+    InvalidStatus,
     InvalidUpgrade,
     NegotiationError,
 )
@@ -471,8 +472,14 @@ def reject(
                 ("Server", USER_AGENT),
             ]
         )
+        response = Response(status.value, status.phrase, headers, body)
+        # When reject() is called from accept(), handshake_exc is already set.
+        # If a user calls reject(), set handshake_exc to guarantee invariant:
+        # "handshake_exc is None if and only if opening handshake succeded."
+        if self.handshake_exc is None:
+            self.handshake_exc = InvalidStatus(response)
         self.logger.info("connection failed (%d %s)", status.value, status.phrase)
-        return Response(status.value, status.phrase, headers, body)
+        return response
 
     def send_response(self, response: Response) -> None:
         """
@@ -497,6 +504,8 @@ def send_response(self, response: Response) -> None:
             self.state = OPEN
         else:
             self.send_eof()
+            self.parser = self.discard()
+            next(self.parser)  # start coroutine
 
     def parse(self) -> Generator[None, None, None]:
         if self.state is CONNECTING:
diff --git a/tests/test_client.py b/tests/test_client.py
index 12fd8726..a843d327 100644
--- a/tests/test_client.py
+++ b/tests/test_client.py
@@ -42,6 +42,7 @@ def test_send_connect(self):
                 f"\r\n".encode()
             ],
         )
+        self.assertFalse(client.close_expected())
 
     def test_connect_request(self):
         with unittest.mock.patch("websockets.client.generate_key", return_value=KEY):
@@ -135,6 +136,8 @@ def test_receive_accept(self):
         )
         [response] = client.events_received()
         self.assertIsInstance(response, Response)
+        self.assertEqual(client.data_to_send(), [])
+        self.assertFalse(client.close_expected())
         self.assertEqual(client.state, OPEN)
 
     def test_receive_reject(self):
@@ -155,6 +158,8 @@ def test_receive_reject(self):
         )
         [response] = client.events_received()
         self.assertIsInstance(response, Response)
+        self.assertEqual(client.data_to_send(), [])
+        self.assertTrue(client.close_expected())
         self.assertEqual(client.state, CONNECTING)
 
     def test_accept_response(self):
diff --git a/tests/test_server.py b/tests/test_server.py
index 43bc03e1..e3e80223 100644
--- a/tests/test_server.py
+++ b/tests/test_server.py
@@ -38,6 +38,8 @@ def test_receive_connect(self):
         )
         [request] = server.events_received()
         self.assertIsInstance(request, Request)
+        self.assertEqual(server.data_to_send(), [])
+        self.assertFalse(server.close_expected())
 
     def test_connect_request(self):
         server = ServerConnection()
@@ -104,6 +106,7 @@ def test_send_accept(self):
                 f"\r\n".encode()
             ],
         )
+        self.assertFalse(server.close_expected())
         self.assertEqual(server.state, OPEN)
 
     def test_send_reject(self):
@@ -126,6 +129,7 @@ def test_send_reject(self):
                 b"",
             ],
         )
+        self.assertTrue(server.close_expected())
         self.assertEqual(server.state, CONNECTING)
 
     def test_accept_response(self):