diff --git a/.github/workflows/core.yml b/.github/workflows/core.yml
index fdfdebc65d..21a64efa96 100644
--- a/.github/workflows/core.yml
+++ b/.github/workflows/core.yml
@@ -55,6 +55,7 @@ jobs:
     - name: Install test requirements
       run: python3 ./devscripts/install_deps.py --include test --include curl-cffi
     - name: Run tests
+      timeout-minutes: 15
       continue-on-error: False
       run: |
         python3 -m yt_dlp -v || true  # Print debug head
diff --git a/.github/workflows/quick-test.yml b/.github/workflows/quick-test.yml
index 3afb51a308..fe2a7e9239 100644
--- a/.github/workflows/quick-test.yml
+++ b/.github/workflows/quick-test.yml
@@ -17,6 +17,7 @@ jobs:
     - name: Install test requirements
       run: python3 ./devscripts/install_deps.py --include test
     - name: Run tests
+      timeout-minutes: 15
       run: |
         python3 -m yt_dlp -v || true
         python3 ./devscripts/run_tests.py core
diff --git a/pyproject.toml b/pyproject.toml
index d5480e1c6d..fe6894a428 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -49,7 +49,7 @@ dependencies = [
     "pycryptodomex",
     "requests>=2.32.2,<3",
     "urllib3>=1.26.17,<3",
-    "websockets>=12.0",
+    "websockets>=13.0",
 ]
 
 [project.optional-dependencies]
diff --git a/test/test_websockets.py b/test/test_websockets.py
index 43f20ac655..06112cc0b8 100644
--- a/test/test_websockets.py
+++ b/test/test_websockets.py
@@ -88,7 +88,7 @@ def create_wss_websocket_server():
     certfn = os.path.join(TEST_DIR, 'testcert.pem')
     sslctx = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
     sslctx.load_cert_chain(certfn, None)
-    return create_websocket_server(ssl_context=sslctx)
+    return create_websocket_server(ssl=sslctx)
 
 
 MTLS_CERT_DIR = os.path.join(TEST_DIR, 'testdata', 'certificate')
@@ -103,7 +103,7 @@ def create_mtls_wss_websocket_server():
     sslctx.load_verify_locations(cafile=cacertfn)
     sslctx.load_cert_chain(certfn, None)
 
-    return create_websocket_server(ssl_context=sslctx)
+    return create_websocket_server(ssl=sslctx)
 
 
 def create_legacy_wss_websocket_server():
@@ -112,7 +112,7 @@ def create_legacy_wss_websocket_server():
     sslctx.maximum_version = ssl.TLSVersion.TLSv1_2
     sslctx.set_ciphers('SHA1:AESCCM:aDSS:eNULL:aNULL')
     sslctx.load_cert_chain(certfn, None)
-    return create_websocket_server(ssl_context=sslctx)
+    return create_websocket_server(ssl=sslctx)
 
 
 def ws_validate_and_send(rh, req):
@@ -139,7 +139,7 @@ class TestWebsSocketRequestHandlerConformance:
         cls.wss_thread, cls.wss_port = create_wss_websocket_server()
         cls.wss_base_url = f'wss://127.0.0.1:{cls.wss_port}'
 
-        cls.bad_wss_thread, cls.bad_wss_port = create_websocket_server(ssl_context=ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER))
+        cls.bad_wss_thread, cls.bad_wss_port = create_websocket_server(ssl=ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER))
         cls.bad_wss_host = f'wss://127.0.0.1:{cls.bad_wss_port}'
 
         cls.mtls_wss_thread, cls.mtls_wss_port = create_mtls_wss_websocket_server()
diff --git a/yt_dlp/networking/_websockets.py b/yt_dlp/networking/_websockets.py
index 492af1154d..21b765b91d 100644
--- a/yt_dlp/networking/_websockets.py
+++ b/yt_dlp/networking/_websockets.py
@@ -47,10 +47,7 @@ from websockets.uri import parse_uri
 # 2: "AttributeError: 'ClientConnection' object has no attribute 'recv_events_exc'. Did you mean: 'recv_events'?"
 import websockets.sync.connection  # isort: split
 with contextlib.suppress(Exception):
-    # > 12.0
     websockets.sync.connection.Connection.recv_exc = None
-    # 12.0
-    websockets.sync.connection.Connection.recv_events_exc = None
 
 
 class WebsocketsResponseAdapter(WebSocketResponse):
@@ -162,7 +159,7 @@ class WebsocketsRH(WebSocketRequestHandler):
                 additional_headers=headers,
                 open_timeout=timeout,
                 user_agent_header=None,
-                ssl_context=ssl_ctx if wsuri.secure else None,
+                ssl=ssl_ctx if wsuri.secure else None,
                 close_timeout=0,  # not ideal, but prevents yt-dlp hanging
             )
             return WebsocketsResponseAdapter(conn, url=request.url)