diff --git a/.circleci/server-test-names.txt b/.circleci/server-test-names.txt
index 124868b1edf..e8db8766831 100644
--- a/.circleci/server-test-names.txt
+++ b/.circleci/server-test-names.txt
@@ -32,9 +32,9 @@ jwt-cookie
 jwt-cookie-unauthorized-role
 # cors-domains
 # auth-webhook-cookie
-ws-init-cookie-read-cors-enabled
-ws-init-cookie-noread
-ws-init-cookie-read-cors-disabled
+# ws-init-cookie-read-cors-enabled
+# ws-init-cookie-noread
+# ws-init-cookie-read-cors-disabled
 # ws-graphql-api-disabled
 # ws-metadata-api-disabled
 # remote-schema-permissions
diff --git a/server/tests-py/conftest.py b/server/tests-py/conftest.py
index 5fe92dec273..1acbc857831 100644
--- a/server/tests-py/conftest.py
+++ b/server/tests-py/conftest.py
@@ -3,7 +3,6 @@ import http.server
 import inspect
 import os
 import pytest
-import re
 import socket
 import sqlalchemy
 import sys
@@ -53,13 +52,6 @@ def pytest_addoption(parser):
         "--hge-jwt-conf", metavar="HGE_JWT_CONF", help="The JWT conf", required=False
     )
 
-    parser.addoption(
-        "--test-ws-init-cookie",
-        metavar="read|noread",
-        required=False,
-        help="Run testcases for testing cookie sending over websockets"
-    )
-
     parser.addoption(
         "--test-hge-scale-url",
         metavar="<url>",
diff --git a/server/tests-py/context.py b/server/tests-py/context.py
index 530d4db2b4c..4a9ae5064ad 100644
--- a/server/tests-py/context.py
+++ b/server/tests-py/context.py
@@ -856,8 +856,6 @@ class HGECtx:
         self.engine = sqlalchemy.create_engine(self.metadata_schema_url)
         self.meta = sqlalchemy.schema.MetaData()
 
-        self.ws_read_cookie = config.getoption('--test-ws-init-cookie')
-
         self.hge_scale_url = config.getoption('--test-hge-scale-url')
         self.avoid_err_msg_checks = config.getoption('--avoid-error-message-checks')
         self.pro_tests = config.getoption('--pro-tests')
diff --git a/server/tests-py/test_websocket_init_cookie.py b/server/tests-py/test_websocket_init_cookie.py
index db01610ac06..0ab1ff5f7d8 100644
--- a/server/tests-py/test_websocket_init_cookie.py
+++ b/server/tests-py/test_websocket_init_cookie.py
@@ -3,17 +3,20 @@ from urllib.parse import urlparse
 
 import websocket
 import pytest
-from context import PytestConf
-
-if not PytestConf.config.getoption("--test-ws-init-cookie"):
-    pytest.skip("--test-ws-init-cookie flag is missing, skipping tests", allow_module_level=True)
 
 def url(hge_ctx):
     ws_url = urlparse(hge_ctx.hge_url)._replace(scheme='ws', path='/v1alpha1/graphql')
     return ws_url.geturl()
 
-@pytest.mark.usefixtures('auth_hook')
-class TestWebsocketInitCookie():
+# The tests below would ideally use parameterization rather than subclassing,
+# but that doesn't work because of `hge_fixture_env`, which creates a "soft"
+# dependency between the environment variables and `hge_server`. Parameterizing
+# the former *should* force the latter to be recreated for each new set of
+# environment variables, but `hge_server` isn't actually aware there's a
+# dependency. See `TestParameterizedFixtures` in test_tests.py for more
+# information.
+
+class AbstractTestWebsocketInitCookie:
     """
     test if cookie is sent when initing the websocket connection, is our auth
     webhook receiving the cookie
@@ -43,9 +46,7 @@ class TestWebsocketInitCookie():
         ws.send(json.dumps(payload))
         return ws
 
-    def test_websocket_init_cookie_used(self, hge_ctx):
-        if hge_ctx.ws_read_cookie == 'noread':
-            pytest.skip('cookie is not to be read')
+    def _test_received_data(self, hge_ctx):
         ws = self._send_query(hge_ctx)
         it = 0
         while True:
@@ -55,38 +56,45 @@ class TestWebsocketInitCookie():
                 assert 'person' in frame['payload']['data']
                 break
             elif it == 10:
-                print('max try over')
-                assert False
-                break
+                assert False, f'max try over: {raw}'
             elif frame['type'] == 'connection_error' or frame['type'] == 'error':
-                print(frame)
-                assert False
-                break
+                assert False, f'connection error: {raw}'
             it = it + 1
 
-    def test_websocket_init_cookie_not_used(self, hge_ctx):
-        if hge_ctx.ws_read_cookie == 'read':
-            pytest.skip('cookie is read')
-
+    def _test_received_connection_error(self, hge_ctx):
         ws = self._send_query(hge_ctx)
         it = 0
         while True:
             raw = ws.recv()
             frame = json.loads(raw)
             if frame['type'] ==  'data':
-                print('got data')
-                assert False
-                break
+                assert False, f'got data: {raw}'
             elif it == 10:
-                print('max try over')
-                assert False
-                break
+                assert False, f'max try over: {raw}'
             elif frame['type'] == 'connection_error':
-                print(frame)
                 assert frame['payload'] == 'Authentication hook unauthorized this request'
                 break
             elif frame['type'] == 'error':
-                print(frame)
-                assert False
-                break
+                assert False, f'error: {raw}'
             it = it + 1
+
+@pytest.mark.admin_secret
+@pytest.mark.usefixtures('auth_hook')
+class TestWebsocketInitCookieReadWithCorsEnabled(AbstractTestWebsocketInitCookie):
+    def test_websocket_init_cookie_used(self, hge_ctx):
+        self._test_received_data(hge_ctx)
+
+@pytest.mark.admin_secret
+@pytest.mark.usefixtures('auth_hook')
+@pytest.mark.hge_env('HASURA_GRAPHQL_DISABLE_CORS', 'true')
+class TestWebsocketInitCookieNotReadWithCorsDisabled(AbstractTestWebsocketInitCookie):
+    def test_websocket_init_cookie_not_used(self, hge_ctx):
+        self._test_received_connection_error(hge_ctx)
+
+@pytest.mark.admin_secret
+@pytest.mark.usefixtures('auth_hook')
+@pytest.mark.hge_env('HASURA_GRAPHQL_DISABLE_CORS', 'true')
+@pytest.mark.hge_env('HASURA_GRAPHQL_WS_READ_COOKIE', 'true')
+class TestWebsocketInitCookieReadWithCorsDisabledWhenRequired(AbstractTestWebsocketInitCookie):
+    def test_websocket_init_cookie_not_used(self, hge_ctx):
+        self._test_received_data(hge_ctx)