diff --git a/test/test_http_proxy.py b/test/test_http_proxy.py
index 63fe94405..058c6b253 100644
--- a/test/test_http_proxy.py
+++ b/test/test_http_proxy.py
@@ -172,7 +172,7 @@ def __init__(self, request, *args, **kwargs):
         certfn = os.path.join(TEST_DIR, 'testcert.pem')
         sslctx = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
         sslctx.load_cert_chain(certfn, None)
-        if SSLTransport:
+        if isinstance(request, ssl.SSLSocket) and SSLTransport:
             request = SSLTransport(request, ssl_context=sslctx, server_side=True)
         else:
             request = sslctx.wrap_socket(request, server_side=True)
@@ -213,10 +213,7 @@ def __init__(self, request, *args, **kwargs):
         certfn = os.path.join(TEST_DIR, 'testcert.pem')
         sslctx = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
         sslctx.load_cert_chain(certfn, None)
-        if SSLTransport:
-            request = SSLTransport(request, ssl_context=sslctx, server_side=True)
-        else:
-            request = sslctx.wrap_socket(request, server_side=True)
+        request = sslctx.wrap_socket(request, server_side=True)
         self._original_request = request
         super().__init__(request, *args, **kwargs)
 
@@ -244,7 +241,6 @@ def proxy_server(proxy_server_class, request_handler, bind_ip=None, **proxy_serv
     finally:
         server.shutdown()
         server.server_close()
-        server_thread.join(2.0)
 
 
 class HTTPProxyTestContext(abc.ABC):
@@ -393,11 +389,11 @@ def test_http_with_idn(self, handler, ctx):
         ('Websockets', 'ws'),
         ('Websockets', 'wss')
     ], indirect=True)
-@pytest.mark.skip_handler_if(
-    'Websockets', lambda request:
-        (platform.python_implementation() == 'PyPy'
-         and request.getfixturevalue('ctx').REQUEST_PROTO == 'wss'),
-    'PyPy sometimes fails with wss tests, unknown reason')
+# @pytest.mark.skip_handler_if(
+#     'Websockets', lambda request:
+#         (platform.python_implementation() == 'PyPy'
+#          and request.getfixturevalue('ctx').REQUEST_PROTO == 'wss'),
+#     'PyPy sometimes fails with wss tests, unknown reason')
 class TestHTTPConnectProxy:
     def test_http_connect_no_auth(self, handler, ctx):
         with ctx.http_server(HTTPConnectProxyHandler) as server_address:
diff --git a/yt_dlp/networking/_websockets.py b/yt_dlp/networking/_websockets.py
index 0de81773d..29f1858c8 100644
--- a/yt_dlp/networking/_websockets.py
+++ b/yt_dlp/networking/_websockets.py
@@ -199,20 +199,21 @@ def _send(self, request):
         proxy = select_proxy(request.url, self._get_proxies(request))
 
         ssl_context = None
+        sock = self._make_sock(proxy, request.url, timeout)
         if parse_uri(request.url).secure:
-            if WebsocketsSSLContext is not None:
-                ssl_context = WebsocketsSSLContext(self._make_sslcontext())
-            else:
-                ssl_context = self._make_sslcontext()
+            ssl_context = self._make_sslcontext()
+            if isinstance(sock, ssl.SSLSocket) and WebsocketsSSLContext:  # tls in tls
+                ssl_context = WebsocketsSSLContext(ssl_context)
+
         try:
             conn = websockets.sync.client.connect(
-                sock=self._make_sock(proxy, request.url, timeout),
+                sock=sock,
                 uri=request.url,
                 additional_headers=headers,
                 open_timeout=timeout,
                 user_agent_header=None,
                 ssl_context=ssl_context,
-                close_timeout=0.1,  # not ideal, but prevents yt-dlp hanging
+                close_timeout=0,  # not ideal, but prevents yt-dlp hanging
             )
             return WebsocketsResponseAdapter(conn, url=request.url)