diff --git a/swh/dataset/luigi.py b/swh/dataset/luigi.py
--- a/swh/dataset/luigi.py
+++ b/swh/dataset/luigi.py
@@ -401,14 +401,16 @@
 
         # recursively copy local files to S3, and end with stamps and export metadata
         for format_ in self.formats:
-            for object_type in self.object_types:
-                local_dir = self.local_export_path / format_.name / object_type.name
-                s3_dir = f"{self.s3_export_path}/{format_.name}/{object_type.name}"
-                if not local_dir.exists():
-                    # intermediary object types (eg. origin_visit, origin_visit_status)
-                    # do not have their own directory
+            for dirname in os.listdir(self.local_export_path / format_.name):
+                if dirname == "stamps":
+                    # used as stamps while exporting, pointless to copy them
                     continue
-                status_message = f"Uploading {format_.name}/{object_type.name}/"
+                if dirname == "meta":
+                    # used as final stamp; copy it at the end
+                    continue
+                local_dir = self.local_export_path / format_.name / dirname
+                s3_dir = f"{self.s3_export_path}/{format_.name}/{dirname}"
+                status_message = f"Uploading {format_.name}/{dirname}/"
                 self.set_status_message(status_message)
                 for file_ in tqdm.tqdm(
                     list(os.listdir(local_dir)),
@@ -471,6 +473,8 @@
 
     def run(self) -> None:
         """Copies all files: first the export itself, then :file:`meta.json`."""
+        import collections
+
         import luigi.contrib.s3
         import tqdm
 
@@ -478,16 +482,18 @@
 
         # recursively copy local files to S3, and end with export metadata
         for format_ in self.formats:
-            for object_type in self.object_types:
-                local_dir = self.local_export_path / format_.name / object_type.name
-                s3_dir = f"{self.s3_export_path}/{format_.name}/{object_type.name}"
-                files = list(client.list(s3_dir))
-                if not files:
-                    # intermediary object types (eg. origin_visit, origin_visit_status)
-                    # do not have their own directory
-                    continue
-                local_dir.mkdir(parents=True, exist_ok=True)
-                status_message = f"Downloading {format_.name}/{object_type.name}/"
+            local_dir = self.local_export_path / format_.name
+            s3_dir = f"{self.s3_export_path}/{format_.name}"
+            files = list(client.list(s3_dir))
+            assert files, "No files found"
+
+            files_by_type = collections.defaultdict(list)
+            for file in files:
+                files_by_type[file.split("/")[0]].append(file)
+
+            for (object_type, files) in files_by_type.items():
+                (local_dir / object_type).mkdir(parents=True, exist_ok=True)
+                status_message = f"Downloading {format_.name}/{object_type}/"
                 self.set_status_message(status_message)
                 for file_ in tqdm.tqdm(
                     files,