diff --git a/src/test/regress/expected/stats.out b/src/test/regress/expected/stats.out
index f5be70fe7c..a811265d69 100644
--- a/src/test/regress/expected/stats.out
+++ b/src/test/regress/expected/stats.out
@@ -37,17 +37,33 @@ SELECT t.seq_scan, t.seq_tup_read, t.idx_scan, t.idx_tup_fetch,
 create function wait_for_stats() returns void as $$
 declare
   start_time timestamptz := clock_timestamp();
-  updated bool;
+  updated1 bool;
+  updated2 bool;
+  updated3 bool;
 begin
   -- we don't want to wait forever; loop will exit after 30 seconds
   for i in 1 .. 300 loop
 
-    -- check to see if indexscan has been sensed
-    SELECT (st.idx_scan >= pr.idx_scan + 1) INTO updated
+    -- With parallel query, the seqscan and indexscan on tenk2 might be done
+    -- in parallel worker processes, which will send their stats counters
+    -- asynchronously to what our own session does.  So we must check for
+    -- those counts to be registered separately from the update counts.
+
+    -- check to see if seqscan has been sensed
+    SELECT (st.seq_scan >= pr.seq_scan + 1) INTO updated1
       FROM pg_stat_user_tables AS st, pg_class AS cl, prevstats AS pr
      WHERE st.relname='tenk2' AND cl.relname='tenk2';
 
-    exit when updated;
+    -- check to see if indexscan has been sensed
+    SELECT (st.idx_scan >= pr.idx_scan + 1) INTO updated2
+      FROM pg_stat_user_tables AS st, pg_class AS cl, prevstats AS pr
+     WHERE st.relname='tenk2' AND cl.relname='tenk2';
+
+    -- check to see if updates have been sensed
+    SELECT (n_tup_ins > 0) INTO updated3
+      FROM pg_stat_user_tables WHERE relname='trunc_stats_test';
+
+    exit when updated1 and updated2 and updated3;
 
     -- wait a little
     perform pg_sleep(0.1);
@@ -127,7 +143,7 @@ SELECT count(*) FROM tenk2 WHERE unique1 = 1;
      1
 (1 row)
 
--- force the rate-limiting logic in pgstat_report_tabstat() to time out
+-- force the rate-limiting logic in pgstat_report_stat() to time out
 -- and send a message
 SELECT pg_sleep(1.0);
  pg_sleep 
diff --git a/src/test/regress/sql/stats.sql b/src/test/regress/sql/stats.sql
index cd2d5927bc..b3e2efa535 100644
--- a/src/test/regress/sql/stats.sql
+++ b/src/test/regress/sql/stats.sql
@@ -32,17 +32,33 @@ SELECT t.seq_scan, t.seq_tup_read, t.idx_scan, t.idx_tup_fetch,
 create function wait_for_stats() returns void as $$
 declare
   start_time timestamptz := clock_timestamp();
-  updated bool;
+  updated1 bool;
+  updated2 bool;
+  updated3 bool;
 begin
   -- we don't want to wait forever; loop will exit after 30 seconds
   for i in 1 .. 300 loop
 
-    -- check to see if indexscan has been sensed
-    SELECT (st.idx_scan >= pr.idx_scan + 1) INTO updated
+    -- With parallel query, the seqscan and indexscan on tenk2 might be done
+    -- in parallel worker processes, which will send their stats counters
+    -- asynchronously to what our own session does.  So we must check for
+    -- those counts to be registered separately from the update counts.
+
+    -- check to see if seqscan has been sensed
+    SELECT (st.seq_scan >= pr.seq_scan + 1) INTO updated1
       FROM pg_stat_user_tables AS st, pg_class AS cl, prevstats AS pr
      WHERE st.relname='tenk2' AND cl.relname='tenk2';
 
-    exit when updated;
+    -- check to see if indexscan has been sensed
+    SELECT (st.idx_scan >= pr.idx_scan + 1) INTO updated2
+      FROM pg_stat_user_tables AS st, pg_class AS cl, prevstats AS pr
+     WHERE st.relname='tenk2' AND cl.relname='tenk2';
+
+    -- check to see if updates have been sensed
+    SELECT (n_tup_ins > 0) INTO updated3
+      FROM pg_stat_user_tables WHERE relname='trunc_stats_test';
+
+    exit when updated1 and updated2 and updated3;
 
     -- wait a little
     perform pg_sleep(0.1);
@@ -121,7 +137,7 @@ SELECT count(*) FROM tenk2;
 -- do an indexscan
 SELECT count(*) FROM tenk2 WHERE unique1 = 1;
 
--- force the rate-limiting logic in pgstat_report_tabstat() to time out
+-- force the rate-limiting logic in pgstat_report_stat() to time out
 -- and send a message
 SELECT pg_sleep(1.0);