diff --git a/swh/web/tests/conftest.py b/swh/web/tests/conftest.py
--- a/swh/web/tests/conftest.py
+++ b/swh/web/tests/conftest.py
@@ -10,7 +10,9 @@
 import sys
 from typing import Any, Dict, List, Optional
 
-from hypothesis import HealthCheck, settings
+from hypothesis import HealthCheck
+from hypothesis import __version_info__ as hypothesis_version
+from hypothesis import settings
 import pytest
 
 from django.core.cache import cache
@@ -34,20 +36,18 @@
 # Register some hypothesis profiles
 settings.register_profile("default", settings())
 
+suppress_health_check = [HealthCheck.too_slow, HealthCheck.filter_too_much]
+if hypothesis_version >= (5, 49):
+    suppress_health_check.append(HealthCheck.function_scoped_fixture)
+
 settings.register_profile(
-    "swh-web",
-    settings(
-        deadline=None,
-        suppress_health_check=[HealthCheck.too_slow, HealthCheck.filter_too_much],
-    ),
+    "swh-web", settings(deadline=None, suppress_health_check=suppress_health_check,),
 )
 
 settings.register_profile(
     "swh-web-fast",
     settings(
-        deadline=None,
-        max_examples=1,
-        suppress_health_check=[HealthCheck.too_slow, HealthCheck.filter_too_much],
+        deadline=None, max_examples=1, suppress_health_check=suppress_health_check,
     ),
 )