diff --git a/conftest.py b/conftest.py
index 71afc47..cd5ed25 100644
--- a/conftest.py
+++ b/conftest.py
@@ -1,68 +1,67 @@
 # Copyright (C) 2019-2020  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 import os
 import pytest
 import yaml
 
 from typing import Any, Dict
 
-from swh.storage.tests.conftest import *  # noqa
-from swh.scheduler.tests.conftest import *  # noqa
+from swh.scheduler.tests.conftest import swh_app  # noqa
 
 
 @pytest.fixture
 def swh_loader_config(swh_storage_postgresql) -> Dict[str, Any]:
     return {
         "storage": {
             "cls": "pipeline",
             "steps": [
                 {"cls": "retry"},
                 {"cls": "filter"},
                 {"cls": "buffer"},
                 {
                     "cls": "local",
                     "db": swh_storage_postgresql.dsn,
                     "objstorage": {"cls": "memory", "args": {}},
                 },
             ],
         },
         "deposit": {
             "url": "https://deposit.softwareheritage.org/1/private",
             "auth": {"username": "user", "password": "pass",},
         },
     }
 
 
 @pytest.fixture
 def swh_config(swh_loader_config, monkeypatch, tmp_path):
     conffile = os.path.join(str(tmp_path), "loader.yml")
     with open(conffile, "w") as f:
         f.write(yaml.dump(swh_loader_config))
     monkeypatch.setenv("SWH_CONFIG_FILENAME", conffile)
     return conffile
 
 
 @pytest.fixture(autouse=True, scope="session")
 def swh_proxy():
     """Automatically inject this fixture in all tests to ensure no outside
        connection takes place.
 
     """
     os.environ["http_proxy"] = "http://localhost:999"
     os.environ["https_proxy"] = "http://localhost:999"
 
 
 @pytest.fixture(scope="session")  # type: ignore  # expected redefinition
 def celery_includes():
     return [
         "swh.loader.package.archive.tasks",
         "swh.loader.package.cran.tasks",
         "swh.loader.package.debian.tasks",
         "swh.loader.package.deposit.tasks",
         "swh.loader.package.npm.tasks",
         "swh.loader.package.pypi.tasks",
         "swh.loader.package.nixguix.tasks",
     ]
diff --git a/requirements-swh.txt b/requirements-swh.txt
index 9cf7880..2d0f2ec 100644
--- a/requirements-swh.txt
+++ b/requirements-swh.txt
@@ -1,4 +1,4 @@
 swh.core >= 0.0.75
 swh.model >= 0.3.7
-swh.scheduler
-swh.storage >= 0.8.0
+swh.scheduler >= 0.4.0
+swh.storage >= 0.10.1
diff --git a/requirements-test.txt b/requirements-test.txt
index 368666f..aab3d89 100644
--- a/requirements-test.txt
+++ b/requirements-test.txt
@@ -1,6 +1,6 @@
 pytest
 pytest-mock
-pytest-postgresql >= 2.1.0
 requests_mock
 swh-core[testing]
 swh-scheduler[testing]
+swh-storage[testing]
diff --git a/tox.ini b/tox.ini
index 456c7aa..e5faf28 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,36 +1,37 @@
 [tox]
 envlist=black,flake8,mypy,py3
 
 [testenv]
 extras =
   testing
 deps =
   swh.core[http]
+  swh.storage[testing]  # otherwise, somehow pytest-postgresql is not seen
   pytest-cov
   dev: pdbpp
 commands =
   pytest \
   !dev: --cov={envsitepackagesdir}/swh/loader/ --cov-branch \
          {envsitepackagesdir}/swh/loader/ {posargs}
 
 [testenv:black]
 skip_install = true
 deps =
   black
 commands =
   {envpython} -m black --check swh
 
 [testenv:flake8]
 skip_install = true
 deps =
   flake8
 commands =
   {envpython} -m flake8
 
 [testenv:mypy]
 extras =
   testing
 deps =
   mypy
 commands =
   mypy swh