diff --git a/swh/objstorage/__init__.py b/swh/objstorage/__init__.py
--- a/swh/objstorage/__init__.py
+++ b/swh/objstorage/__init__.py
@@ -3,14 +3,14 @@
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
-from .objstorage import ObjStorage
-from .objstorage_pathslicing import PathSlicingObjStorage
-from .objstorage_in_memory import InMemoryObjStorage
-from .api.client import RemoteObjStorage
-from .multiplexer import MultiplexerObjStorage, StripingObjStorage
-from .multiplexer.filter import add_filters
-
-from swh.objstorage.objstorage_weed import WeedObjStorage
+from swh.objstorage.objstorage import ObjStorage, ID_HASH_LENGTH  # noqa
+from swh.objstorage.backends.pathslicing import PathSlicingObjStorage
+from swh.objstorage.backends.in_memory import InMemoryObjStorage
+from swh.objstorage.api.client import RemoteObjStorage
+from swh.objstorage.multiplexer import (
+    MultiplexerObjStorage, StripingObjStorage)
+from swh.objstorage.multiplexer.filter import add_filters
+from swh.objstorage.backends.seaweed import WeedObjStorage
 
 __all__ = ['get_objstorage', 'ObjStorage']
 
@@ -26,7 +26,7 @@
 }
 
 try:
-    from swh.objstorage.cloud.objstorage_azure import (
+    from swh.objstorage.backends.azure import (
         AzureCloudObjStorage,
         PrefixedAzureCloudObjStorage,
     )
@@ -37,13 +37,13 @@
     _STORAGE_CLASSES_MISSING['azure-prefixed'] = e.args[0]
 
 try:
-    from swh.objstorage.objstorage_rados import RADOSObjStorage
+    from swh.objstorage.backends.rados import RADOSObjStorage
     _STORAGE_CLASSES['rados'] = RADOSObjStorage
 except ImportError as e:
     _STORAGE_CLASSES_MISSING['rados'] = e.args[0]
 
 try:
-    from swh.objstorage.cloud.objstorage_cloud import (
+    from swh.objstorage.backends.libcloud import (
         AwsCloudObjStorage,
         OpenStackCloudObjStorage,
     )
diff --git a/swh/objstorage/backends/__init__.py b/swh/objstorage/backends/__init__.py
new file mode 100644
diff --git a/swh/objstorage/cloud/objstorage_azure.py b/swh/objstorage/backends/azure.py
rename from swh/objstorage/cloud/objstorage_azure.py
rename to swh/objstorage/backends/azure.py
diff --git a/swh/objstorage/objstorage_in_memory.py b/swh/objstorage/backends/in_memory.py
rename from swh/objstorage/objstorage_in_memory.py
rename to swh/objstorage/backends/in_memory.py
diff --git a/swh/objstorage/cloud/objstorage_cloud.py b/swh/objstorage/backends/libcloud.py
rename from swh/objstorage/cloud/objstorage_cloud.py
rename to swh/objstorage/backends/libcloud.py
diff --git a/swh/objstorage/objstorage_pathslicing.py b/swh/objstorage/backends/pathslicing.py
rename from swh/objstorage/objstorage_pathslicing.py
rename to swh/objstorage/backends/pathslicing.py
--- a/swh/objstorage/objstorage_pathslicing.py
+++ b/swh/objstorage/backends/pathslicing.py
@@ -15,9 +15,10 @@
 
 from swh.model import hashutil
 
-from .objstorage import (ObjStorage, compute_hash, ID_HASH_ALGO,
-                         ID_HASH_LENGTH, DEFAULT_CHUNK_SIZE, DEFAULT_LIMIT)
-from .exc import ObjNotFoundError, Error
+from swh.objstorage.objstorage import (
+    ObjStorage, compute_hash, ID_HASH_ALGO,
+    ID_HASH_LENGTH, DEFAULT_CHUNK_SIZE, DEFAULT_LIMIT)
+from swh.objstorage.exc import ObjNotFoundError, Error
 
 
 GZIP_BUFSIZ = 1048576
diff --git a/swh/objstorage/objstorage_rados.py b/swh/objstorage/backends/rados.py
rename from swh/objstorage/objstorage_rados.py
rename to swh/objstorage/backends/rados.py
diff --git a/swh/objstorage/objstorage_weed.py b/swh/objstorage/backends/seaweed.py
rename from swh/objstorage/objstorage_weed.py
rename to swh/objstorage/backends/seaweed.py
diff --git a/swh/objstorage/cloud/__init__.py b/swh/objstorage/cloud/__init__.py
deleted file mode 100644
--- a/swh/objstorage/cloud/__init__.py
+++ /dev/null
@@ -1,9 +0,0 @@
-from .objstorage_cloud import AwsCloudObjStorage, OpenStackCloudObjStorage
-from .objstorage_azure import AzureCloudObjStorage
-
-
-__all__ = [
-    'AwsCloudObjStorage',
-    'OpenStackCloudObjStorage',
-    'AzureCloudObjStorage',
-]
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
@@ -68,7 +68,7 @@
     def setUp(self):
         super().setUp()
         patcher = patch(
-            'swh.objstorage.cloud.objstorage_azure.BlockBlobService',
+            'swh.objstorage.backends.azure.BlockBlobService',
             MockBlockBlobService,
         )
         patcher.start()
@@ -86,7 +86,7 @@
     def setUp(self):
         super().setUp()
         patcher = patch(
-            'swh.objstorage.cloud.objstorage_azure.BlockBlobService',
+            'swh.objstorage.backends.azure.BlockBlobService',
             MockBlockBlobService,
         )
         patcher.start()
diff --git a/swh/objstorage/tests/test_objstorage_cloud.py b/swh/objstorage/tests/test_objstorage_cloud.py
--- a/swh/objstorage/tests/test_objstorage_cloud.py
+++ b/swh/objstorage/tests/test_objstorage_cloud.py
@@ -12,7 +12,7 @@
 from libcloud.storage.types import (ContainerDoesNotExistError,
                                     ObjectDoesNotExistError)
 from swh.model import hashutil
-from swh.objstorage.cloud.objstorage_cloud import CloudObjStorage
+from swh.objstorage.backends.libcloud import CloudObjStorage
 
 from .objstorage_testing import ObjStorageTestFixture
 
diff --git a/swh/objstorage/tests/test_objstorage_instantiation.py b/swh/objstorage/tests/test_objstorage_instantiation.py
--- a/swh/objstorage/tests/test_objstorage_instantiation.py
+++ b/swh/objstorage/tests/test_objstorage_instantiation.py
@@ -9,7 +9,7 @@
 
 from swh.objstorage import get_objstorage
 from swh.objstorage.api.client import RemoteObjStorage
-from swh.objstorage.objstorage_pathslicing import PathSlicingObjStorage
+from swh.objstorage.backends.pathslicing import PathSlicingObjStorage
 
 
 class TestObjStorageInitialization(unittest.TestCase):