diff --git a/src/test/regress/parallel_schedule b/src/test/regress/parallel_schedule
index 43a7bcff9aca61840c0fede33983764cd0c83afc..96976ccc9f19794456b1e2a238e2bf1c8f2200c1 100644
--- a/src/test/regress/parallel_schedule
+++ b/src/test/regress/parallel_schedule
@@ -74,4 +74,7 @@ test: select_views portals_p2 rules foreign_key cluster
 # The sixth group of parallel test
 # ----------
 # "plpgsql" cannot run concurrently with "rules"
-test: limit plpgsql copy2 temp domain rangefuncs prepare without_oid conversion truncate alter_table sequence polymorphism stats
+test: limit plpgsql copy2 temp domain rangefuncs prepare without_oid conversion truncate alter_table sequence polymorphism
+
+# run stats by itself because its delay may be insufficient under heavy load
+test: stats