diff --git a/trio_websocket/_impl.py b/trio_websocket/_impl.py
index 36d6cbf..3aceda6 100644
--- a/trio_websocket/_impl.py
+++ b/trio_websocket/_impl.py
@@ -1018,6 +1018,12 @@ async def _close_web_socket(self, code, reason=None):
         exc = ConnectionClosed(self._close_reason)
         logger.debug('%s websocket closed %r', self, exc)
         await self._send_channel.aclose()
+        # RFC: "When a server is instructed to Close the WebSocket Connection
+        #   it SHOULD initiate a TCP Close immediately, and when a client is
+        #   instructed to do the same, it SHOULD wait for a TCP Close from the
+        #   server."
+        if self.is_server:
+            await self._close_stream()
 
     async def _get_request(self):
         '''