diff --git a/swh/scheduler/journal_client.py b/swh/scheduler/journal_client.py
--- a/swh/scheduler/journal_client.py
+++ b/swh/scheduler/journal_client.py
@@ -51,7 +51,8 @@
     elif position_offset < 5:
         result = 2
     else:
-        result = 4 ** (position_offset - 4)
+        exp = max(10, position_offset - 4)
+        result = 4 ** exp
     return result