diff --git a/swh/objstorage/backends/azure.py b/swh/objstorage/backends/azure.py
--- a/swh/objstorage/backends/azure.py
+++ b/swh/objstorage/backends/azure.py
@@ -3,7 +3,6 @@
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
-import gzip
 import string
 from itertools import dropwhile, islice, product
 
@@ -11,7 +10,8 @@
 from azure.common import AzureMissingResourceHttpError
 import requests
 
-from swh.objstorage.objstorage import ObjStorage, compute_hash, DEFAULT_LIMIT
+from swh.objstorage.objstorage import (ObjStorage, compute_hash, DEFAULT_LIMIT,
+                                       compressors, decompressors)
 from swh.objstorage.exc import ObjNotFoundError, Error
 from swh.model import hashutil
 
@@ -20,7 +20,8 @@
     """ObjStorage with azure abilities.
 
     """
-    def __init__(self, account_name, api_secret_key, container_name, **kwargs):
+    def __init__(self, account_name, api_secret_key, container_name,
+                 compression='gzip', **kwargs):
         super().__init__(**kwargs)
         self.block_blob_service = BlockBlobService(
             account_name=account_name,
@@ -28,6 +29,7 @@
             request_session=requests.Session(),
         )
         self.container_name = container_name
+        self.compression = compression
 
     def get_blob_service(self, hex_obj_id):
         """Get the block_blob_service and container that contains the object with
@@ -96,12 +98,16 @@
 
         hex_obj_id = self._internal_id(obj_id)
 
-        # Send the gzipped content
+        # Send the compressed content
+        compressor = compressors[self.compression]()
+        blob = [compressor.compress(content), compressor.flush()]
+
         service, container = self.get_blob_service(hex_obj_id)
         service.create_blob_from_bytes(
             container_name=container,
             blob_name=hex_obj_id,
-            blob=gzip.compress(content))
+            blob=b''.join(blob),
+        )
 
         return obj_id
 
@@ -124,7 +130,11 @@
         except AzureMissingResourceHttpError:
             raise ObjNotFoundError(obj_id)
 
-        return gzip.decompress(blob.content)
+        decompressor = decompressors[self.compression]()
+        ret = decompressor.decompress(blob.content)
+        if decompressor.unused_data:
+            raise Error('Corrupt object %s: trailing data found' % hex_obj_id)
+        return ret
 
     def check(self, obj_id):
         """Check the content integrity.
@@ -177,10 +187,12 @@
           api_secret_key: <api_secret_key>
           container_name: <container_name>
     """
-    def __init__(self, accounts, **kwargs):
+    def __init__(self, accounts, compression='gzip', **kwargs):
         # shortcut AzureCloudObjStorage __init__
         ObjStorage.__init__(self, **kwargs)
 
+        self.compression = compression
+
         # Definition sanity check
         prefix_lengths = set(len(prefix) for prefix in accounts)
         if not len(prefix_lengths) == 1:
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
@@ -7,11 +7,13 @@
 from collections import defaultdict
 from unittest.mock import patch
 
-from typing import Any, Dict
+from typing import Any, Dict, Optional
 
 from azure.common import AzureMissingResourceHttpError
 from swh.model.hashutil import hash_to_hex
+
 from swh.objstorage import get_objstorage
+from swh.objstorage.objstorage import decompressors
 
 from .objstorage_testing import ObjStorageTestFixture
 
@@ -66,6 +68,7 @@
 
 
 class TestAzureCloudObjStorage(ObjStorageTestFixture, unittest.TestCase):
+    compression = None  # type: Optional[str]
 
     def setUp(self):
         super().setUp()
@@ -80,8 +83,38 @@
             'account_name': 'account-name',
             'api_secret_key': 'api-secret-key',
             'container_name': 'container-name',
+            'compression': self.compression,
         })
 
+    def test_compression(self):
+        content, obj_id = self.hash_content(b'test content is compressed')
+        self.storage.add(content, obj_id=obj_id)
+
+        blob_service, container = self.storage.get_blob_service(obj_id)
+        internal_id = self.storage._internal_id(obj_id)
+
+        raw_blob = blob_service.get_blob_to_bytes(container, internal_id)
+
+        d = decompressors[self.compression]()
+        assert d.decompress(raw_blob.content) == content
+        assert d.unused_data == b''
+
+
+class TestAzureCloudObjStorageGzip(TestAzureCloudObjStorage):
+    compression = 'gzip'
+
+
+class TestAzureCloudObjStorageZlib(TestAzureCloudObjStorage):
+    compression = 'zlib'
+
+
+class TestAzureCloudObjStorageLzma(TestAzureCloudObjStorage):
+    compression = 'lzma'
+
+
+class TestAzureCloudObjStorageBz2(TestAzureCloudObjStorage):
+    compression = 'bz2'
+
 
 class TestPrefixedAzureCloudObjStorage(ObjStorageTestFixture,
                                        unittest.TestCase):