diff --git a/swh/storage/tests/algos/test_snapshot.py b/swh/storage/tests/algos/test_snapshot.py
--- a/swh/storage/tests/algos/test_snapshot.py
+++ b/swh/storage/tests/algos/test_snapshot.py
@@ -3,7 +3,7 @@
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
-from hypothesis import given
+from hypothesis import HealthCheck, given, settings
 import pytest
 
 from swh.model.hypothesis_strategies import branch_names, branch_targets, snapshots
@@ -32,6 +32,7 @@
     }
 
 
+@settings(suppress_health_check=[HealthCheck.function_scoped_fixture])
 @given(snapshot=snapshots(min_size=0, max_size=10, only_objects=False))
 def test_snapshot_small(swh_storage, snapshot):  # noqa
     swh_storage.snapshot_add([snapshot])
@@ -40,6 +41,7 @@
     assert snapshot == returned_snapshot
 
 
+@settings(suppress_health_check=[HealthCheck.function_scoped_fixture])
 @given(branch_name=branch_names(), branch_target=branch_targets(only_objects=True))
 def test_snapshot_large(swh_storage, branch_name, branch_target):  # noqa
     snapshot = Snapshot(
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: