diff --git a/scripts/replay-curtin-log.py b/scripts/replay-curtin-log.py
index 358f5a7a..6f1b0570 100644
--- a/scripts/replay-curtin-log.py
+++ b/scripts/replay-curtin-log.py
@@ -36,8 +36,12 @@ class FakeEvent:
     def as_dict(self):
         return self._ev_dict
 
+prev_ev = None
 for line in open(json_file):
     d = json.loads(line.strip())
     ev = FakeEvent(d)
-    events.report_event(ev)
-    time.sleep(random.expovariate(2))
+    if prev_ev is not None:
+        events.report_event(prev_ev)
+        time.sleep(min((ev.timestamp - prev_ev.timestamp)/4, 2))
+    prev_ev = ev
+events.report_event(prev_ev)