diff --git a/swh/vault/cookers/git_bare.py b/swh/vault/cookers/git_bare.py
--- a/swh/vault/cookers/git_bare.py
+++ b/swh/vault/cookers/git_bare.py
@@ -304,6 +304,7 @@
             assert_never(self.obj_type, f"Unexpected root object type: {self.obj_type}")
 
     def load_objects(self) -> None:
+        nb_loaded = 0
         while self._rel_stack or self._rev_stack or self._dir_stack or self._cnt_stack:
 
             nb_remaining = (
@@ -318,25 +319,29 @@
             self.backend.set_progress(
                 self.BUNDLE_TYPE,
                 self.swhid,
-                f"Processing... {len(self._seen)} objects processed\n"
+                f"Processing... {nb_loaded} objects processed\n"
                 f"Over {nb_remaining} remaining",
             )
 
             release_ids = self._pop(self._rel_stack, RELEASE_BATCH_SIZE)
             if release_ids:
                 self.load_releases(release_ids)
+                nb_loaded += len(release_ids)
 
             revision_ids = self._pop(self._rev_stack, REVISION_BATCH_SIZE)
             if revision_ids:
                 self.load_revisions(revision_ids)
+                nb_loaded += len(revision_ids)
 
             directory_ids = self._pop(self._dir_stack, DIRECTORY_BATCH_SIZE)
             if directory_ids:
                 self.load_directories(directory_ids)
+                nb_loaded += len(directory_ids)
 
             content_ids = self._pop(self._cnt_stack, CONTENT_BATCH_SIZE)
             if content_ids:
                 self.load_contents(content_ids)
+                nb_loaded += len(content_ids)
 
     def push_revision_subgraph(self, obj_id: Sha1Git) -> None:
         """Fetches a revision and all its children, and writes them to disk"""