diff --git a/swh/storage/tests/storage_tests.py b/swh/storage/tests/storage_tests.py
--- a/swh/storage/tests/storage_tests.py
+++ b/swh/storage/tests/storage_tests.py
@@ -420,7 +420,10 @@
         assert missing == [cont2.hashes()]
 
     @pytest.mark.property_based
-    @settings(deadline=None)  # this test is very slow
+    @settings(
+        deadline=None,  # this test is very slow
+        suppress_health_check=[HealthCheck.function_scoped_fixture],
+    )
     @given(
         strategies.sets(
             elements=strategies.sampled_from(["sha256", "sha1_git", "blake2s256"]),
@@ -451,6 +454,7 @@
             ) == set(missing_per_hash[hash])
 
     @pytest.mark.property_based
+    @settings(suppress_health_check=[HealthCheck.function_scoped_fixture])
     @given(
         strategies.sets(
             elements=strategies.sampled_from(["sha256", "sha1_git", "blake2s256"]),
@@ -3920,7 +3924,12 @@
         )
         assert swh_storage.origin_count("github", regexp=True, with_visit=True) == 1
 
-    @settings(suppress_health_check=[HealthCheck.too_slow])
+    @settings(
+        suppress_health_check=[
+            HealthCheck.too_slow,
+            HealthCheck.function_scoped_fixture,
+        ]
+    )
     @given(strategies.lists(objects(split_content=True), max_size=2))
     def test_add_arbitrary(self, swh_storage, objects):
         for (obj_type, obj) in objects: