diff --git a/testing/web-platform/tests/tools/wptserve/wptserve/server.py b/testing/web-platform/tests/tools/wptserve/wptserve/server.py
index 6375beea5651..7446d7818abf 100644
--- a/testing/web-platform/tests/tools/wptserve/wptserve/server.py
+++ b/testing/web-platform/tests/tools/wptserve/wptserve/server.py
@@ -10,7 +10,7 @@ import time
 import traceback
 import uuid
 from collections import OrderedDict
-from queue import Queue
+from queue import Empty, Queue
 
 from h2.config import H2Configuration
 from h2.connection import H2Connection
@@ -412,12 +412,11 @@ class Http2WebTestRequestHandler(BaseWebTestRequestHandler):
             self.logger.error('(%s) Closing Connection - \n%s' % (self.uid, str(e)))
             if not self.close_connection:
                 self.close_connection = True
-                for stream_id, (thread, queue) in stream_queues.items():
-                    queue.put(None)
         except Exception as e:
             self.logger.error('(%s) Unexpected Error - \n%s' % (self.uid, str(e)))
         finally:
             for stream_id, (thread, queue) in stream_queues.items():
+                queue.put(None)
                 thread.join()
 
     def _is_extended_connect_frame(self, frame):
@@ -459,6 +458,9 @@ class Http2WebTestRequestHandler(BaseWebTestRequestHandler):
     def _stream_ws_thread(self, stream_id, queue):
         frame = queue.get(True, None)
 
+        if frame is None:
+            return
+
         rfile, wfile = os.pipe()
         rfile, wfile = os.fdopen(rfile, 'rb'), os.fdopen(wfile, 'wb', 0)  # needs to be unbuffer for websockets
         stream_handler = H2HandlerCopy(self, frame, rfile)
@@ -511,7 +513,10 @@ class Http2WebTestRequestHandler(BaseWebTestRequestHandler):
         t.start()
 
         while not self.close_connection:
-            frame = queue.get(True, None)
+            try:
+                frame = queue.get(True, 1)
+            except Empty:
+                continue
 
             if isinstance(frame, DataReceived):
                 wfile.write(frame.data)
@@ -558,8 +563,11 @@ class Http2WebTestRequestHandler(BaseWebTestRequestHandler):
         response = None
         req_handler = None
         while not self.close_connection:
-            # Wait for next frame, blocking
-            frame = queue.get(True, None)
+            try:
+                frame = queue.get(True, 1)
+            except Empty:
+                # Restart to check for close_connection
+                continue
 
             self.logger.debug('(%s - %s) %s' % (self.uid, stream_id, str(frame)))
 
@@ -598,7 +606,12 @@ class Http2WebTestRequestHandler(BaseWebTestRequestHandler):
                 request.frames.append(frame)
 
             if hasattr(frame, "stream_ended") and frame.stream_ended:
-                self.finish_handling(request, response, req_handler)
+                try:
+                    self.finish_handling(request, response, req_handler)
+                except StreamClosedError:
+                    self.logger.debug('(%s - %s) Unable to write response; stream closed' %
+                                      (self.uid, stream_id))
+                    break
 
     def frame_handler(self, request, response, handler):
         try: