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
@@ -14,7 +14,7 @@
     ContainerSasPermissions,
     generate_container_sas,
 )
-from azure.core.exceptions import ResourceNotFoundError
+from azure.core.exceptions import ResourceExistsError, ResourceNotFoundError
 
 from swh.objstorage.objstorage import (
     ObjStorage,
@@ -210,7 +210,14 @@
         data += compressor.flush()
 
         client = self.get_blob_client(hex_obj_id)
-        client.upload_blob(data=data, length=len(data))
+        try:
+            client.upload_blob(data=data, length=len(data))
+        except ResourceExistsError:
+            # There's a race condition between check_presence and upload_blob,
+            # that we can't get rid of as the azure api doesn't allow atomic
+            # replaces or renaming a blob. As the restore operation explicitly
+            # removes the blob, it should be safe to just ignore the error.
+            pass
 
         return obj_id
 
diff --git a/swh/objstorage/tests/objstorage_testing.py b/swh/objstorage/tests/objstorage_testing.py
--- a/swh/objstorage/tests/objstorage_testing.py
+++ b/swh/objstorage/tests/objstorage_testing.py
@@ -36,6 +36,15 @@
         self.assertEqual(obj_id, r)
         self.assertContentMatch(obj_id, content)
 
+    def test_add_twice(self):
+        content, obj_id = self.hash_content(b"add_twice")
+        r = self.storage.add(content, obj_id=obj_id)
+        self.assertEqual(obj_id, r)
+        self.assertContentMatch(obj_id, content)
+        r = self.storage.add(content, obj_id=obj_id, check_presence=False)
+        self.assertEqual(obj_id, r)
+        self.assertContentMatch(obj_id, content)
+
     def test_add_big(self):
         content, obj_id = self.hash_content(b"add_big" * 1024 * 1024)
         r = self.storage.add(content, obj_id=obj_id)
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
@@ -9,7 +9,7 @@
 from unittest.mock import patch
 from urllib.parse import urlparse, parse_qs
 
-from azure.core.exceptions import ResourceNotFoundError
+from azure.core.exceptions import ResourceExistsError, ResourceNotFoundError
 import pytest
 
 from swh.model.hashutil import hash_to_hex
@@ -48,7 +48,7 @@
 
     def upload_blob(self, data, length=None):
         if self.blob in self.container.blobs:
-            raise ValueError("Blob already exists")
+            raise ResourceExistsError("Blob already exists")
 
         if length is not None and length != len(data):
             raise ValueError("Wrong length for blob data!")