diff --git a/src/backend/executor/nodeAgg.c b/src/backend/executor/nodeAgg.c
index 8a0bd887bf..fe5c47e533 100644
--- a/src/backend/executor/nodeAgg.c
+++ b/src/backend/executor/nodeAgg.c
@@ -1758,9 +1758,15 @@ hashagg_recompile_expressions(AggState *aggstate, bool minslot, bool nullcheck)
 		const TupleTableSlotOps *outerops = aggstate->ss.ps.outerops;
 		bool		outerfixed = aggstate->ss.ps.outeropsfixed;
 		bool		dohash = true;
-		bool		dosort;
+		bool		dosort = false;
 
-		dosort = aggstate->aggstrategy == AGG_MIXED ? true : false;
+		/*
+		 * If minslot is true, that means we are processing a spilled batch
+		 * (inside agg_refill_hash_table()), and we must not advance the
+		 * sorted grouping sets.
+		 */
+		if (aggstate->aggstrategy == AGG_MIXED && !minslot)
+			dosort = true;
 
 		/* temporarily change the outerops while compiling the expression */
 		if (minslot)
@@ -2601,11 +2607,15 @@ agg_refill_hash_table(AggState *aggstate)
 						batch->used_bits, &aggstate->hash_mem_limit,
 						&aggstate->hash_ngroups_limit, NULL);
 
-	/* there could be residual pergroup pointers; clear them */
-	for (int setoff = 0;
-		 setoff < aggstate->maxsets + aggstate->num_hashes;
-		 setoff++)
-		aggstate->all_pergroups[setoff] = NULL;
+	/*
+	 * Each batch only processes one grouping set; set the rest to NULL so
+	 * that advance_aggregates() knows to ignore them. We don't touch
+	 * pergroups for sorted grouping sets here, because they will be needed if
+	 * we rescan later. The expressions for sorted grouping sets will not be
+	 * evaluated after we recompile anyway.
+	 */
+	MemSet(aggstate->hash_pergroup, 0,
+		   sizeof(AggStatePerGroup) * aggstate->num_hashes);
 
 	/* free memory and reset hash tables */
 	ReScanExprContext(aggstate->hashcontext);
diff --git a/src/test/regress/expected/groupingsets.out b/src/test/regress/expected/groupingsets.out
index 701d52b465..c00b2dd648 100644
--- a/src/test/regress/expected/groupingsets.out
+++ b/src/test/regress/expected/groupingsets.out
@@ -1665,6 +1665,213 @@ select v||'a', case when grouping(v||'a') = 1 then 1 else 0 end, count(*)
           |    1 |     2
 (4 rows)
 
+-- Bug #16784
+CREATE TABLE bug_16784(i INT, j INT);
+ANALYZE bug_16784;
+ALTER TABLE bug_16784 SET (autovacuum_enabled = 'false');
+UPDATE pg_class SET reltuples = 10 WHERE relname='bug_16784';
+INSERT INTO bug_16784 SELECT g/10, g FROM generate_series(1,40) g;
+SET work_mem='64kB';
+explain (costs off) select * from
+  (values (1),(2)) v(a),
+  lateral (select v.a, i, j, count(*) from
+             bug_16784 group by cube(i,j)) s
+  order by v.a, i, j;
+                        QUERY PLAN                        
+----------------------------------------------------------
+ Sort
+   Sort Key: "*VALUES*".column1, bug_16784.i, bug_16784.j
+   ->  Nested Loop
+         ->  Values Scan on "*VALUES*"
+         ->  MixedAggregate
+               Hash Key: bug_16784.i, bug_16784.j
+               Hash Key: bug_16784.i
+               Hash Key: bug_16784.j
+               Group Key: ()
+               ->  Seq Scan on bug_16784
+(10 rows)
+
+select * from
+  (values (1),(2)) v(a),
+  lateral (select a, i, j, count(*) from
+             bug_16784 group by cube(i,j)) s
+  order by v.a, i, j;
+ a | a | i | j  | count 
+---+---+---+----+-------
+ 1 | 1 | 0 |  1 |     1
+ 1 | 1 | 0 |  2 |     1
+ 1 | 1 | 0 |  3 |     1
+ 1 | 1 | 0 |  4 |     1
+ 1 | 1 | 0 |  5 |     1
+ 1 | 1 | 0 |  6 |     1
+ 1 | 1 | 0 |  7 |     1
+ 1 | 1 | 0 |  8 |     1
+ 1 | 1 | 0 |  9 |     1
+ 1 | 1 | 0 |    |     9
+ 1 | 1 | 1 | 10 |     1
+ 1 | 1 | 1 | 11 |     1
+ 1 | 1 | 1 | 12 |     1
+ 1 | 1 | 1 | 13 |     1
+ 1 | 1 | 1 | 14 |     1
+ 1 | 1 | 1 | 15 |     1
+ 1 | 1 | 1 | 16 |     1
+ 1 | 1 | 1 | 17 |     1
+ 1 | 1 | 1 | 18 |     1
+ 1 | 1 | 1 | 19 |     1
+ 1 | 1 | 1 |    |    10
+ 1 | 1 | 2 | 20 |     1
+ 1 | 1 | 2 | 21 |     1
+ 1 | 1 | 2 | 22 |     1
+ 1 | 1 | 2 | 23 |     1
+ 1 | 1 | 2 | 24 |     1
+ 1 | 1 | 2 | 25 |     1
+ 1 | 1 | 2 | 26 |     1
+ 1 | 1 | 2 | 27 |     1
+ 1 | 1 | 2 | 28 |     1
+ 1 | 1 | 2 | 29 |     1
+ 1 | 1 | 2 |    |    10
+ 1 | 1 | 3 | 30 |     1
+ 1 | 1 | 3 | 31 |     1
+ 1 | 1 | 3 | 32 |     1
+ 1 | 1 | 3 | 33 |     1
+ 1 | 1 | 3 | 34 |     1
+ 1 | 1 | 3 | 35 |     1
+ 1 | 1 | 3 | 36 |     1
+ 1 | 1 | 3 | 37 |     1
+ 1 | 1 | 3 | 38 |     1
+ 1 | 1 | 3 | 39 |     1
+ 1 | 1 | 3 |    |    10
+ 1 | 1 | 4 | 40 |     1
+ 1 | 1 | 4 |    |     1
+ 1 | 1 |   |  1 |     1
+ 1 | 1 |   |  2 |     1
+ 1 | 1 |   |  3 |     1
+ 1 | 1 |   |  4 |     1
+ 1 | 1 |   |  5 |     1
+ 1 | 1 |   |  6 |     1
+ 1 | 1 |   |  7 |     1
+ 1 | 1 |   |  8 |     1
+ 1 | 1 |   |  9 |     1
+ 1 | 1 |   | 10 |     1
+ 1 | 1 |   | 11 |     1
+ 1 | 1 |   | 12 |     1
+ 1 | 1 |   | 13 |     1
+ 1 | 1 |   | 14 |     1
+ 1 | 1 |   | 15 |     1
+ 1 | 1 |   | 16 |     1
+ 1 | 1 |   | 17 |     1
+ 1 | 1 |   | 18 |     1
+ 1 | 1 |   | 19 |     1
+ 1 | 1 |   | 20 |     1
+ 1 | 1 |   | 21 |     1
+ 1 | 1 |   | 22 |     1
+ 1 | 1 |   | 23 |     1
+ 1 | 1 |   | 24 |     1
+ 1 | 1 |   | 25 |     1
+ 1 | 1 |   | 26 |     1
+ 1 | 1 |   | 27 |     1
+ 1 | 1 |   | 28 |     1
+ 1 | 1 |   | 29 |     1
+ 1 | 1 |   | 30 |     1
+ 1 | 1 |   | 31 |     1
+ 1 | 1 |   | 32 |     1
+ 1 | 1 |   | 33 |     1
+ 1 | 1 |   | 34 |     1
+ 1 | 1 |   | 35 |     1
+ 1 | 1 |   | 36 |     1
+ 1 | 1 |   | 37 |     1
+ 1 | 1 |   | 38 |     1
+ 1 | 1 |   | 39 |     1
+ 1 | 1 |   | 40 |     1
+ 1 | 1 |   |    |    40
+ 2 | 2 | 0 |  1 |     1
+ 2 | 2 | 0 |  2 |     1
+ 2 | 2 | 0 |  3 |     1
+ 2 | 2 | 0 |  4 |     1
+ 2 | 2 | 0 |  5 |     1
+ 2 | 2 | 0 |  6 |     1
+ 2 | 2 | 0 |  7 |     1
+ 2 | 2 | 0 |  8 |     1
+ 2 | 2 | 0 |  9 |     1
+ 2 | 2 | 0 |    |     9
+ 2 | 2 | 1 | 10 |     1
+ 2 | 2 | 1 | 11 |     1
+ 2 | 2 | 1 | 12 |     1
+ 2 | 2 | 1 | 13 |     1
+ 2 | 2 | 1 | 14 |     1
+ 2 | 2 | 1 | 15 |     1
+ 2 | 2 | 1 | 16 |     1
+ 2 | 2 | 1 | 17 |     1
+ 2 | 2 | 1 | 18 |     1
+ 2 | 2 | 1 | 19 |     1
+ 2 | 2 | 1 |    |    10
+ 2 | 2 | 2 | 20 |     1
+ 2 | 2 | 2 | 21 |     1
+ 2 | 2 | 2 | 22 |     1
+ 2 | 2 | 2 | 23 |     1
+ 2 | 2 | 2 | 24 |     1
+ 2 | 2 | 2 | 25 |     1
+ 2 | 2 | 2 | 26 |     1
+ 2 | 2 | 2 | 27 |     1
+ 2 | 2 | 2 | 28 |     1
+ 2 | 2 | 2 | 29 |     1
+ 2 | 2 | 2 |    |    10
+ 2 | 2 | 3 | 30 |     1
+ 2 | 2 | 3 | 31 |     1
+ 2 | 2 | 3 | 32 |     1
+ 2 | 2 | 3 | 33 |     1
+ 2 | 2 | 3 | 34 |     1
+ 2 | 2 | 3 | 35 |     1
+ 2 | 2 | 3 | 36 |     1
+ 2 | 2 | 3 | 37 |     1
+ 2 | 2 | 3 | 38 |     1
+ 2 | 2 | 3 | 39 |     1
+ 2 | 2 | 3 |    |    10
+ 2 | 2 | 4 | 40 |     1
+ 2 | 2 | 4 |    |     1
+ 2 | 2 |   |  1 |     1
+ 2 | 2 |   |  2 |     1
+ 2 | 2 |   |  3 |     1
+ 2 | 2 |   |  4 |     1
+ 2 | 2 |   |  5 |     1
+ 2 | 2 |   |  6 |     1
+ 2 | 2 |   |  7 |     1
+ 2 | 2 |   |  8 |     1
+ 2 | 2 |   |  9 |     1
+ 2 | 2 |   | 10 |     1
+ 2 | 2 |   | 11 |     1
+ 2 | 2 |   | 12 |     1
+ 2 | 2 |   | 13 |     1
+ 2 | 2 |   | 14 |     1
+ 2 | 2 |   | 15 |     1
+ 2 | 2 |   | 16 |     1
+ 2 | 2 |   | 17 |     1
+ 2 | 2 |   | 18 |     1
+ 2 | 2 |   | 19 |     1
+ 2 | 2 |   | 20 |     1
+ 2 | 2 |   | 21 |     1
+ 2 | 2 |   | 22 |     1
+ 2 | 2 |   | 23 |     1
+ 2 | 2 |   | 24 |     1
+ 2 | 2 |   | 25 |     1
+ 2 | 2 |   | 26 |     1
+ 2 | 2 |   | 27 |     1
+ 2 | 2 |   | 28 |     1
+ 2 | 2 |   | 29 |     1
+ 2 | 2 |   | 30 |     1
+ 2 | 2 |   | 31 |     1
+ 2 | 2 |   | 32 |     1
+ 2 | 2 |   | 33 |     1
+ 2 | 2 |   | 34 |     1
+ 2 | 2 |   | 35 |     1
+ 2 | 2 |   | 36 |     1
+ 2 | 2 |   | 37 |     1
+ 2 | 2 |   | 38 |     1
+ 2 | 2 |   | 39 |     1
+ 2 | 2 |   | 40 |     1
+ 2 | 2 |   |    |    40
+(172 rows)
+
 --
 -- Compare results between plans using sorting and plans using hash
 -- aggregation. Force spilling in both cases by setting work_mem low
diff --git a/src/test/regress/sql/groupingsets.sql b/src/test/regress/sql/groupingsets.sql
index d4e5628eba..93b33c65d1 100644
--- a/src/test/regress/sql/groupingsets.sql
+++ b/src/test/regress/sql/groupingsets.sql
@@ -457,6 +457,27 @@ select v||'a', case when grouping(v||'a') = 1 then 1 else 0 end, count(*)
   from unnest(array[1,1], array['a','b']) u(i,v)
  group by rollup(i, v||'a') order by 1,3;
 
+-- Bug #16784
+CREATE TABLE bug_16784(i INT, j INT);
+ANALYZE bug_16784;
+ALTER TABLE bug_16784 SET (autovacuum_enabled = 'false');
+UPDATE pg_class SET reltuples = 10 WHERE relname='bug_16784';
+
+INSERT INTO bug_16784 SELECT g/10, g FROM generate_series(1,40) g;
+
+SET work_mem='64kB';
+
+explain (costs off) select * from
+  (values (1),(2)) v(a),
+  lateral (select v.a, i, j, count(*) from
+             bug_16784 group by cube(i,j)) s
+  order by v.a, i, j;
+select * from
+  (values (1),(2)) v(a),
+  lateral (select a, i, j, count(*) from
+             bug_16784 group by cube(i,j)) s
+  order by v.a, i, j;
+
 --
 -- Compare results between plans using sorting and plans using hash
 -- aggregation. Force spilling in both cases by setting work_mem low