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
@@ -121,7 +121,7 @@
                 )
 
         super().__init__(**kwargs)
-        self.container_client = ContainerClient.from_container_url(container_url)
+        self.container_url = container_url
         self.compression = compression
 
     def get_container_client(self, hex_obj_id):
@@ -132,7 +132,7 @@
         client according to the prefix of the object id.
 
         """
-        return self.container_client
+        return ContainerClient.from_container_url(self.container_url)
 
     def get_blob_client(self, hex_obj_id):
         """Get the azure blob client for the given hex obj id"""
@@ -142,7 +142,7 @@
 
     def get_all_container_clients(self):
         """Get all active block_blob_services"""
-        yield self.container_client
+        yield self.get_container_client("")
 
     def _internal_id(self, obj_id):
         """Internal id is the hex version in objstorage.
@@ -318,7 +318,7 @@
 
         do_warning = False
 
-        self.prefixes = {}
+        self.container_urls = {}
         for prefix, container_url in accounts.items():
             if isinstance(container_url, dict):
                 do_warning = True
@@ -328,7 +328,7 @@
                     container_name=container_url["container_name"],
                     access_policy="full",
                 )
-            self.prefixes[prefix] = ContainerClient.from_container_url(container_url)
+            self.container_urls[prefix] = container_url
 
         if do_warning:
             warnings.warn(
@@ -341,10 +341,13 @@
         """Get the block_blob_service and container that contains the object with
         internal id hex_obj_id
         """
-        return self.prefixes[hex_obj_id[: self.prefix_len]]
+        prefix = hex_obj_id[: self.prefix_len]
+        return ContainerClient.from_container_url(self.container_urls[prefix])
 
     def get_all_container_clients(self):
         """Get all active container clients"""
         # iterate on items() to sort blob services;
         # needed to be able to paginate in the list_content() method
-        yield from (v for _, v in sorted(self.prefixes.items()))
+        yield from (
+            self.get_container_client(prefix) for prefix in sorted(self.container_urls)
+        )
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
@@ -1,9 +1,10 @@
-# Copyright (C) 2016-2020  The Software Heritage developers
+# Copyright (C) 2016-2021  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 base64
+import collections
 from dataclasses import dataclass
 import unittest
 from unittest.mock import patch
@@ -67,27 +68,32 @@
         del self.container.blobs[self.blob]
 
 
-class MockContainerClient:
-    def __init__(self, container_url):
-        self.container_url = container_url
-        self.blobs = {}
+def get_MockContainerClient():
+    blobs = collections.defaultdict(dict)  # {container_url: {blob_id: blob}}
 
-    @classmethod
-    def from_container_url(cls, container_url):
-        return cls(container_url)
+    class MockContainerClient:
+        def __init__(self, container_url):
+            self.container_url = container_url
+            self.blobs = blobs[self.container_url]
 
-    def get_container_properties(self):
-        return {"exists": True}
+        @classmethod
+        def from_container_url(cls, container_url):
+            return cls(container_url)
+
+        def get_container_properties(self):
+            return {"exists": True}
+
+        def get_blob_client(self, blob):
+            return MockBlobClient(self, blob)
 
-    def get_blob_client(self, blob):
-        return MockBlobClient(self, blob)
+        def list_blobs(self):
+            for obj in sorted(self.blobs):
+                yield MockListedObject(obj)
 
-    def list_blobs(self):
-        for obj in sorted(self.blobs):
-            yield MockListedObject(obj)
+        def delete_blob(self, blob):
+            self.get_blob_client(blob.name).delete_blob()
 
-    def delete_blob(self, blob):
-        self.get_blob_client(blob.name).delete_blob()
+    return MockContainerClient
 
 
 class TestAzureCloudObjStorage(ObjStorageTestFixture, unittest.TestCase):
@@ -95,8 +101,9 @@
 
     def setUp(self):
         super().setUp()
+        ContainerClient = get_MockContainerClient()
         patcher = patch(
-            "swh.objstorage.backends.azure.ContainerClient", MockContainerClient,
+            "swh.objstorage.backends.azure.ContainerClient", ContainerClient
         )
         patcher.start()
         self.addCleanup(patcher.stop)
@@ -161,8 +168,9 @@
 class TestPrefixedAzureCloudObjStorage(ObjStorageTestFixture, unittest.TestCase):
     def setUp(self):
         super().setUp()
+        self.ContainerClient = get_MockContainerClient()
         patcher = patch(
-            "swh.objstorage.backends.azure.ContainerClient", MockContainerClient
+            "swh.objstorage.backends.azure.ContainerClient", self.ContainerClient
         )
         patcher.start()
         self.addCleanup(patcher.stop)
@@ -193,7 +201,7 @@
             hex_obj_id = hash_to_hex(obj_id)
             prefix = hex_obj_id[0]
             self.assertTrue(
-                self.storage.prefixes[prefix]
+                self.ContainerClient(self.storage.container_urls[prefix])
                 .get_blob_client(hex_obj_id)
                 .get_blob_properties()
             )
@@ -231,7 +239,7 @@
 
 def test_bwcompat_args(monkeypatch):
     monkeypatch.setattr(
-        swh.objstorage.backends.azure, "ContainerClient", MockContainerClient,
+        swh.objstorage.backends.azure, "ContainerClient", get_MockContainerClient(),
     )
 
     with pytest.deprecated_call():
@@ -249,7 +257,7 @@
 
 def test_bwcompat_args_prefixed(monkeypatch):
     monkeypatch.setattr(
-        swh.objstorage.backends.azure, "ContainerClient", MockContainerClient,
+        swh.objstorage.backends.azure, "ContainerClient", get_MockContainerClient(),
     )
 
     accounts = {