diff --git a/Makefile.local b/Makefile.local
--- a/Makefile.local
+++ b/Makefile.local
@@ -1,7 +1 @@
-# run only tests that do not require database setup
-test-nodb:
-	$(NOSE) $(NOSEFLAGS) -a '!db'
-
-# run only tests that do require database setup
-test-db:
-	$(NOSE) $(NOSEFLAGS) -a 'db'
+TESTFLAGS=--hypothesis-profile=fast
diff --git a/conftest.py b/conftest.py
new file mode 100644
--- /dev/null
+++ b/conftest.py
@@ -0,0 +1,6 @@
+from hypothesis import settings
+
+# define tests profile. Full documentation is at:
+# https://hypothesis.readthedocs.io/en/latest/settings.html#settings-profiles
+settings.register_profile("fast", max_examples=5, deadline=5000)
+settings.register_profile("slow", max_examples=20, deadline=5000)
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
@@ -7,7 +7,7 @@
 
 import pytest
 
-from hypothesis import given, settings
+from hypothesis import given
 from hypothesis.strategies import (binary, composite, datetimes, dictionaries,
                                    from_regex, none, one_of, sampled_from)
 
@@ -94,6 +94,7 @@
 
 
 @pytest.mark.db
+@pytest.mark.property_based
 class TestSnapshotAllBranches(StorageTestFixture, unittest.TestCase):
     @given(origins(), datetimes(), snapshots(min_size=0, max_size=10,
                                              only_objects=False))
@@ -106,7 +107,6 @@
                                                       snapshot['id'])
         self.assertEqual(snapshot, returned_snapshot)
 
-    @settings(max_examples=5, deadline=5000)
     @given(origins(), datetimes(),
            branch_names(), branch_targets(only_objects=True))
     def test_snapshot_large(self, origin, ts, branch_name, branch_target):
diff --git a/swh/storage/tests/test_storage.py b/swh/storage/tests/test_storage.py
--- a/swh/storage/tests/test_storage.py
+++ b/swh/storage/tests/test_storage.py
@@ -1846,6 +1846,7 @@
         self.assertIsNotNone(o_m1)
 
 
+@pytest.mark.db
 @pytest.mark.property_based
 class PropBasedTestStorage(BaseTestStorage, unittest.TestCase):
     def assert_contents_ok(self, expected_contents, actual_contents,
diff --git a/tox.ini b/tox.ini
--- a/tox.ini
+++ b/tox.ini
@@ -7,7 +7,15 @@
   pytest-cov
   pifpaf
 commands =
-  pifpaf run postgresql -- pytest --cov=swh --cov-branch {posargs}
+  pifpaf run postgresql -- pytest --hypothesis-profile=fast --cov=swh --cov-branch {posargs}
+
+[testenv:py3-slow]
+deps =
+  .[testing]
+  pytest-cov
+  pifpaf
+commands =
+  pifpaf run postgresql -- pytest --hypothesis-profile=slow --cov=swh --cov-branch {posargs}
 
 [testenv:flake8]
 skip_install = true