diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index 81ab12df60c..fb64730a7e1 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -13926,6 +13926,14 @@ ATPostAlterTypeCleanup(List **wqueue, AlteredTableInfo *tab, LOCKMODE lockmode)
 		Oid			relid;
 
 		relid = IndexGetRelation(oldId, false);
+
+		/*
+		 * As above, make sure we have lock on the index's table if it's not
+		 * the same table.
+		 */
+		if (relid != tab->relid)
+			LockRelationOid(relid, AccessExclusiveLock);
+
 		ATPostAlterTypeParse(oldId, relid, InvalidOid,
 							 (char *) lfirst(def_item),
 							 wqueue, lockmode, tab->rewrite);
@@ -13942,6 +13950,20 @@ ATPostAlterTypeCleanup(List **wqueue, AlteredTableInfo *tab, LOCKMODE lockmode)
 		Oid			relid;
 
 		relid = StatisticsGetRelation(oldId, false);
+
+		/*
+		 * As above, make sure we have lock on the statistics object's table
+		 * if it's not the same table.  However, we take
+		 * ShareUpdateExclusiveLock here, aligning with the lock level used in
+		 * CreateStatistics and RemoveStatisticsById.
+		 *
+		 * CAUTION: this should be done after all cases that grab
+		 * AccessExclusiveLock, else we risk causing deadlock due to needing
+		 * to promote our table lock.
+		 */
+		if (relid != tab->relid)
+			LockRelationOid(relid, ShareUpdateExclusiveLock);
+
 		ATPostAlterTypeParse(oldId, relid, InvalidOid,
 							 (char *) lfirst(def_item),
 							 wqueue, lockmode, tab->rewrite);
diff --git a/src/test/regress/expected/alter_table.out b/src/test/regress/expected/alter_table.out
index 9d90d5505a8..7cebd50a673 100644
--- a/src/test/regress/expected/alter_table.out
+++ b/src/test/regress/expected/alter_table.out
@@ -4620,6 +4620,14 @@ create table attbl(a int);
 create table atref(b attbl check ((b).a is not null));
 alter table attbl alter column a type numeric;  -- someday this should work
 ERROR:  cannot alter table "attbl" because column "atref.b" uses its row type
+alter table atref drop constraint atref_b_check;
+create statistics atref_stat on ((b).a is not null) from atref;
+alter table attbl alter column a type numeric;  -- someday this should work
+ERROR:  cannot alter table "attbl" because column "atref.b" uses its row type
+drop statistics atref_stat;
+create index atref_idx on atref (((b).a));
+alter table attbl alter column a type numeric;  -- someday this should work
+ERROR:  cannot alter table "attbl" because column "atref.b" uses its row type
 drop table attbl, atref;
 /* End test case for bug #18970 */
 -- Test that ALTER TABLE rewrite preserves a clustered index
diff --git a/src/test/regress/expected/generated.out b/src/test/regress/expected/generated.out
index a1f67abb688..f7c867e054c 100644
--- a/src/test/regress/expected/generated.out
+++ b/src/test/regress/expected/generated.out
@@ -1190,6 +1190,30 @@ Inherits: gtest30
 
 ALTER TABLE gtest30_1 ALTER COLUMN b DROP EXPRESSION;  -- error
 ERROR:  cannot drop generation expression from inherited column
+-- composite type dependencies
+CREATE TABLE gtest31_1 (a int, b text GENERATED ALWAYS AS ('hello') STORED, c text);
+CREATE TABLE gtest31_2 (x int, y gtest31_1);
+ALTER TABLE gtest31_1 ALTER COLUMN b TYPE varchar;  -- fails
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
+-- bug #18970: these cases are unsupported, but make sure they fail cleanly
+ALTER TABLE gtest31_2 ADD CONSTRAINT cc CHECK ((y).b IS NOT NULL);
+ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello1');
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
+ALTER TABLE gtest31_2 DROP CONSTRAINT cc;
+CREATE STATISTICS gtest31_2_stat ON ((y).b is not null) FROM gtest31_2;
+ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello2');
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
+DROP STATISTICS gtest31_2_stat;
+CREATE INDEX gtest31_2_y_idx ON gtest31_2(((y).b));
+ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello3');
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
+DROP TABLE gtest31_1, gtest31_2;
+-- Check it for a partitioned table, too
+CREATE TABLE gtest31_1 (a int, b text GENERATED ALWAYS AS ('hello') STORED, c text) PARTITION BY LIST (a);
+CREATE TABLE gtest31_2 (x int, y gtest31_1);
+ALTER TABLE gtest31_1 ALTER COLUMN b TYPE varchar;  -- fails
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
+DROP TABLE gtest31_1, gtest31_2;
 -- triggers
 CREATE TABLE gtest26 (
     a int PRIMARY KEY,
diff --git a/src/test/regress/sql/alter_table.sql b/src/test/regress/sql/alter_table.sql
index df08e93b70f..16ed0782fa1 100644
--- a/src/test/regress/sql/alter_table.sql
+++ b/src/test/regress/sql/alter_table.sql
@@ -3032,6 +3032,14 @@ drop table attbl, atref;
 create table attbl(a int);
 create table atref(b attbl check ((b).a is not null));
 alter table attbl alter column a type numeric;  -- someday this should work
+alter table atref drop constraint atref_b_check;
+
+create statistics atref_stat on ((b).a is not null) from atref;
+alter table attbl alter column a type numeric;  -- someday this should work
+drop statistics atref_stat;
+
+create index atref_idx on atref (((b).a));
+alter table attbl alter column a type numeric;  -- someday this should work
 drop table attbl, atref;
 
 /* End test case for bug #18970 */
diff --git a/src/test/regress/sql/generated.sql b/src/test/regress/sql/generated.sql
index ba59325da87..2816ac4a74a 100644
--- a/src/test/regress/sql/generated.sql
+++ b/src/test/regress/sql/generated.sql
@@ -550,6 +550,31 @@ ALTER TABLE ONLY gtest30 ALTER COLUMN b DROP EXPRESSION;  -- error
 \d gtest30_1
 ALTER TABLE gtest30_1 ALTER COLUMN b DROP EXPRESSION;  -- error
 
+-- composite type dependencies
+CREATE TABLE gtest31_1 (a int, b text GENERATED ALWAYS AS ('hello') STORED, c text);
+CREATE TABLE gtest31_2 (x int, y gtest31_1);
+ALTER TABLE gtest31_1 ALTER COLUMN b TYPE varchar;  -- fails
+
+-- bug #18970: these cases are unsupported, but make sure they fail cleanly
+ALTER TABLE gtest31_2 ADD CONSTRAINT cc CHECK ((y).b IS NOT NULL);
+ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello1');
+ALTER TABLE gtest31_2 DROP CONSTRAINT cc;
+
+CREATE STATISTICS gtest31_2_stat ON ((y).b is not null) FROM gtest31_2;
+ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello2');
+DROP STATISTICS gtest31_2_stat;
+
+CREATE INDEX gtest31_2_y_idx ON gtest31_2(((y).b));
+ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello3');
+
+DROP TABLE gtest31_1, gtest31_2;
+
+-- Check it for a partitioned table, too
+CREATE TABLE gtest31_1 (a int, b text GENERATED ALWAYS AS ('hello') STORED, c text) PARTITION BY LIST (a);
+CREATE TABLE gtest31_2 (x int, y gtest31_1);
+ALTER TABLE gtest31_1 ALTER COLUMN b TYPE varchar;  -- fails
+DROP TABLE gtest31_1, gtest31_2;
+
 -- triggers
 CREATE TABLE gtest26 (
     a int PRIMARY KEY,