diff --git a/src/backend/access/heap/vacuumlazy.c b/src/backend/access/heap/vacuumlazy.c
index b1fbfca087e..2cbcf5e5db2 100644
--- a/src/backend/access/heap/vacuumlazy.c
+++ b/src/backend/access/heap/vacuumlazy.c
@@ -1263,9 +1263,12 @@ lazy_scan_heap(LVRelState *vacrel)
 		 * Consider if we definitely have enough space to process TIDs on page
 		 * already.  If we are close to overrunning the available space for
 		 * dead_items TIDs, pause and do a cycle of vacuuming before we tackle
-		 * this page.
+		 * this page. However, let's force at least one page-worth of tuples
+		 * to be stored as to ensure we do at least some work when the memory
+		 * configured is so low that we run out before storing anything.
 		 */
-		if (TidStoreMemoryUsage(vacrel->dead_items) > vacrel->dead_items_info->max_bytes)
+		if (vacrel->dead_items_info->num_items > 0 &&
+			TidStoreMemoryUsage(vacrel->dead_items) > vacrel->dead_items_info->max_bytes)
 		{
 			/*
 			 * Before beginning index vacuuming, we release any pin we may
diff --git a/src/test/regress/expected/vacuum.out b/src/test/regress/expected/vacuum.out
index 1a07dbf67d6..3f91b69b324 100644
--- a/src/test/regress/expected/vacuum.out
+++ b/src/test/regress/expected/vacuum.out
@@ -148,6 +148,10 @@ CREATE INDEX brin_pvactst ON pvactst USING brin (i);
 CREATE INDEX gin_pvactst ON pvactst USING gin (a);
 CREATE INDEX gist_pvactst ON pvactst USING gist (p);
 CREATE INDEX spgist_pvactst ON pvactst USING spgist (p);
+CREATE TABLE pvactst2 (i INT) WITH (autovacuum_enabled = off);
+INSERT INTO pvactst2 SELECT generate_series(1, 1000);
+CREATE INDEX ON pvactst2 (i);
+CREATE INDEX ON pvactst2 (i);
 -- VACUUM invokes parallel index cleanup
 SET min_parallel_index_scan_size to 0;
 VACUUM (PARALLEL 2) pvactst;
@@ -167,6 +171,13 @@ VACUUM (PARALLEL) pvactst; -- error, cannot use PARALLEL option without parallel
 ERROR:  parallel option requires a value between 0 and 1024
 LINE 1: VACUUM (PARALLEL) pvactst;
                 ^
+-- Test parallel vacuum using the minimum maintenance_work_mem with and without
+-- dead tuples.
+SET maintenance_work_mem TO 64;
+VACUUM (PARALLEL 2) pvactst2;
+DELETE FROM pvactst2 WHERE i < 1000;
+VACUUM (PARALLEL 2) pvactst2;
+RESET maintenance_work_mem;
 -- Test different combinations of parallel and full options for temporary tables
 CREATE TEMPORARY TABLE tmp (a int PRIMARY KEY);
 CREATE INDEX tmp_idx1 ON tmp (a);
@@ -175,6 +186,7 @@ WARNING:  disabling parallel option of vacuum on "tmp" --- cannot vacuum tempora
 VACUUM (PARALLEL 0, FULL TRUE) tmp; -- can specify parallel disabled (even though that's implied by FULL)
 RESET min_parallel_index_scan_size;
 DROP TABLE pvactst;
+DROP TABLE pvactst2;
 -- INDEX_CLEANUP option
 CREATE TABLE no_index_cleanup (i INT PRIMARY KEY, t TEXT);
 -- Use uncompressed data stored in toast.
diff --git a/src/test/regress/sql/vacuum.sql b/src/test/regress/sql/vacuum.sql
index 5e55079e718..058add027f1 100644
--- a/src/test/regress/sql/vacuum.sql
+++ b/src/test/regress/sql/vacuum.sql
@@ -113,6 +113,10 @@ CREATE INDEX brin_pvactst ON pvactst USING brin (i);
 CREATE INDEX gin_pvactst ON pvactst USING gin (a);
 CREATE INDEX gist_pvactst ON pvactst USING gist (p);
 CREATE INDEX spgist_pvactst ON pvactst USING spgist (p);
+CREATE TABLE pvactst2 (i INT) WITH (autovacuum_enabled = off);
+INSERT INTO pvactst2 SELECT generate_series(1, 1000);
+CREATE INDEX ON pvactst2 (i);
+CREATE INDEX ON pvactst2 (i);
 
 -- VACUUM invokes parallel index cleanup
 SET min_parallel_index_scan_size to 0;
@@ -130,6 +134,14 @@ VACUUM (PARALLEL 2, INDEX_CLEANUP FALSE) pvactst;
 VACUUM (PARALLEL 2, FULL TRUE) pvactst; -- error, cannot use both PARALLEL and FULL
 VACUUM (PARALLEL) pvactst; -- error, cannot use PARALLEL option without parallel degree
 
+-- Test parallel vacuum using the minimum maintenance_work_mem with and without
+-- dead tuples.
+SET maintenance_work_mem TO 64;
+VACUUM (PARALLEL 2) pvactst2;
+DELETE FROM pvactst2 WHERE i < 1000;
+VACUUM (PARALLEL 2) pvactst2;
+RESET maintenance_work_mem;
+
 -- Test different combinations of parallel and full options for temporary tables
 CREATE TEMPORARY TABLE tmp (a int PRIMARY KEY);
 CREATE INDEX tmp_idx1 ON tmp (a);
@@ -137,6 +149,7 @@ VACUUM (PARALLEL 1, FULL FALSE) tmp; -- parallel vacuum disabled for temp tables
 VACUUM (PARALLEL 0, FULL TRUE) tmp; -- can specify parallel disabled (even though that's implied by FULL)
 RESET min_parallel_index_scan_size;
 DROP TABLE pvactst;
+DROP TABLE pvactst2;
 
 -- INDEX_CLEANUP option
 CREATE TABLE no_index_cleanup (i INT PRIMARY KEY, t TEXT);