diff --git a/lib/adapter_web_socket_channel.dart b/lib/adapter_web_socket_channel.dart
index 8415f27..d4df1b3 100644
--- a/lib/adapter_web_socket_channel.dart
+++ b/lib/adapter_web_socket_channel.dart
@@ -79,7 +79,6 @@
     }
 
     webSocketFuture.then((webSocket) {
-      var remoteClosed = false;
       webSocket.events.listen((event) {
         switch (event) {
           case TextDataReceived(text: final text):
@@ -87,7 +86,6 @@
           case BinaryDataReceived(data: final data):
             _controller.local.sink.add(data);
           case CloseReceived(code: final code, reason: final reason):
-            remoteClosed = true;
             _closeCode = code;
             _closeReason = reason;
             _controller.local.sink.close();
@@ -105,13 +103,15 @@
             default:
               throw UnsupportedError('Cannot send ${obj.runtimeType}');
           }
-        } on WebSocketConnectionClosed catch (_) {
+        } on WebSocketConnectionClosed {
           // There is nowhere to surface this error; `_controller.local.sink`
           // has already been closed.
         }
-      }, onDone: () {
-        if (!remoteClosed) {
-          webSocket.close(_localCloseCode, _localCloseReason);
+      }, onDone: () async {
+        try {
+          await webSocket.close(_localCloseCode, _localCloseReason);
+        } on WebSocketConnectionClosed {
+          // It is not an error to close an already-closed `WebSocketChannel`.
         }
       });
       _protocol = webSocket.protocol;
diff --git a/pubspec.yaml b/pubspec.yaml
index d198922..6b8ae39 100644
--- a/pubspec.yaml
+++ b/pubspec.yaml
@@ -14,7 +14,7 @@
   crypto: ^3.0.0
   stream_channel: ^2.1.0
   web: ^0.5.0
-  web_socket: ^0.1.1
+  web_socket: ^0.1.3
 
 dev_dependencies:
   dart_flutter_team_lints: ^2.0.0