diff --git a/setup.py b/setup.py
--- a/setup.py
+++ b/setup.py
@@ -44,6 +44,7 @@
     author_email='swh-devel@inria.fr',
     url='https://forge.softwareheritage.org/diffusion/DOBJS',
     packages=find_packages(),
+    python_requires='>=3.6',
     install_requires=parse_requirements() + parse_requirements('swh'),
     setup_requires=['vcversioner'],
     extras_require={'testing': parse_requirements('test')},
diff --git a/swh/__init__.py b/swh/__init__.py
--- a/swh/__init__.py
+++ b/swh/__init__.py
@@ -1,4 +1,4 @@
 from pkgutil import extend_path
 from typing import Iterable
 
-__path__ = extend_path(__path__, __name__)  # type: Iterable[str]
+__path__: Iterable[str] = extend_path(__path__, __name__)
diff --git a/swh/objstorage/__init__.py b/swh/objstorage/__init__.py
--- a/swh/objstorage/__init__.py
+++ b/swh/objstorage/__init__.py
@@ -18,13 +18,16 @@
 __all__ = ['get_objstorage', 'ObjStorage']
 
 
-_STORAGE_CLASSES = {
+_STORAGE_CLASSES: Dict[
+    str,
+    Union[type, Callable[..., type]]
+] = {
     'pathslicing': PathSlicingObjStorage,
     'remote': RemoteObjStorage,
     'memory': InMemoryObjStorage,
     'weed': WeedObjStorage,
     'random': RandomGeneratorObjStorage,
-}  # type: Dict[str, Union[type, Callable[..., type]]]
+}
 
 _STORAGE_CLASSES_MISSING = {
 }
diff --git a/swh/objstorage/tests/test_objstorage_azure.py b/swh/objstorage/tests/test_objstorage_azure.py
--- a/swh/objstorage/tests/test_objstorage_azure.py
+++ b/swh/objstorage/tests/test_objstorage_azure.py
@@ -30,7 +30,7 @@
     """Mock internal azure library which AzureCloudObjStorage depends upon.
 
     """
-    _data = {}  # type: Dict[str, Any]
+    _data: Dict[str, Any] = {}
 
     def __init__(self, account_name, account_key, **kwargs):
         # do not care for the account_name and the api_secret_key here