diff --git a/requirements-test.txt b/requirements-test.txt
--- a/requirements-test.txt
+++ b/requirements-test.txt
@@ -1,4 +1,4 @@
-hypothesis >= 3.11.0, < 6
+hypothesis >= 3.11.0
 pytest
 pytest-mock
 sqlalchemy-stubs
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
@@ -13,7 +13,9 @@
 from typing import Any, ClassVar, Dict, Iterator, Optional
 
 import attr
-from hypothesis import HealthCheck, given, settings, strategies
+from hypothesis import HealthCheck
+from hypothesis import __version_info__ as hypothesis_version
+from hypothesis import given, settings, strategies
 import pytest
 
 from swh.model import from_disk
@@ -43,6 +45,10 @@
     round_to_milliseconds,
 )
 
+function_scoped_fixture_check = (
+    [HealthCheck.function_scoped_fixture] if hypothesis_version >= (5, 49) else []
+)
+
 
 def transform_entries(
     storage: StorageInterface, dir_: Directory, *, prefix: bytes = b""
@@ -424,7 +430,10 @@
         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=function_scoped_fixture_check,
+    )
     @given(
         strategies.sets(
             elements=strategies.sampled_from(["sha256", "sha1_git", "blake2s256"]),
@@ -455,6 +464,7 @@
             ) == set(missing_per_hash[hash])
 
     @pytest.mark.property_based
+    @settings(suppress_health_check=function_scoped_fixture_check,)
     @given(
         strategies.sets(
             elements=strategies.sampled_from(["sha256", "sha1_git", "blake2s256"]),
@@ -3951,7 +3961,9 @@
         )
         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] + function_scoped_fixture_check,
+    )
     @given(strategies.lists(objects(split_content=True), max_size=2))
     def test_add_arbitrary(self, swh_storage, objects):
         for (obj_type, obj) in objects: