diff --git a/contrib/test_decoding/expected/toast.out b/contrib/test_decoding/expected/toast.out
index 91a9a1e86d6..75c4d22d801 100644
--- a/contrib/test_decoding/expected/toast.out
+++ b/contrib/test_decoding/expected/toast.out
@@ -305,6 +305,10 @@ ALTER TABLE toasted_several REPLICA IDENTITY FULL;
 ALTER TABLE toasted_several ALTER COLUMN toasted_key SET STORAGE EXTERNAL;
 ALTER TABLE toasted_several ALTER COLUMN toasted_col1 SET STORAGE EXTERNAL;
 ALTER TABLE toasted_several ALTER COLUMN toasted_col2 SET STORAGE EXTERNAL;
+-- Change the storage of the index back to EXTENDED, separately from
+-- the table.  This is currently not doable via DDL, but it is
+-- supported internally.
+UPDATE pg_attribute SET attstorage = 'x' WHERE attrelid = 'toasted_several_pkey'::regclass AND attname = 'toasted_key';
 INSERT INTO toasted_several(toasted_key) VALUES(repeat('9876543210', 10000));
 SELECT pg_column_size(toasted_key) > 2^16 FROM toasted_several;
  ?column? 
diff --git a/contrib/test_decoding/sql/toast.sql b/contrib/test_decoding/sql/toast.sql
index ef11d2bfff9..016c3ab7842 100644
--- a/contrib/test_decoding/sql/toast.sql
+++ b/contrib/test_decoding/sql/toast.sql
@@ -279,6 +279,11 @@ ALTER TABLE toasted_several ALTER COLUMN toasted_key SET STORAGE EXTERNAL;
 ALTER TABLE toasted_several ALTER COLUMN toasted_col1 SET STORAGE EXTERNAL;
 ALTER TABLE toasted_several ALTER COLUMN toasted_col2 SET STORAGE EXTERNAL;
 
+-- Change the storage of the index back to EXTENDED, separately from
+-- the table.  This is currently not doable via DDL, but it is
+-- supported internally.
+UPDATE pg_attribute SET attstorage = 'x' WHERE attrelid = 'toasted_several_pkey'::regclass AND attname = 'toasted_key';
+
 INSERT INTO toasted_several(toasted_key) VALUES(repeat('9876543210', 10000));
 SELECT pg_column_size(toasted_key) > 2^16 FROM toasted_several;
 
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index 49d7059d535..bc66d6c4f5f 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -6734,6 +6734,7 @@ ATExecSetStorage(Relation rel, const char *colName, Node *newValue, LOCKMODE loc
 	Form_pg_attribute attrtuple;
 	AttrNumber	attnum;
 	ObjectAddress address;
+	ListCell   *lc;
 
 	Assert(IsA(newValue, String));
 	storagemode = strVal(newValue);
@@ -6793,6 +6794,53 @@ ATExecSetStorage(Relation rel, const char *colName, Node *newValue, LOCKMODE loc
 
 	heap_freetuple(tuple);
 
+	/*
+	 * Apply the change to indexes as well (only for simple index columns,
+	 * matching behavior of index.c ConstructTupleDescriptor()).
+	 */
+	foreach(lc, RelationGetIndexList(rel))
+	{
+		Oid         indexoid = lfirst_oid(lc);
+		Relation    indrel;
+		int			i;
+		AttrNumber	indattnum = 0;
+
+		indrel = index_open(indexoid, lockmode);
+
+		for (i = 0; i < indrel->rd_index->indnatts; i++)
+		{
+			if (indrel->rd_index->indkey.values[i] == attnum)
+			{
+				indattnum = i + 1;
+				break;
+			}
+		}
+
+		if (indattnum == 0)
+		{
+			index_close(indrel, lockmode);
+			continue;
+		}
+
+		tuple = SearchSysCacheCopyAttNum(RelationGetRelid(indrel), indattnum);
+
+		if (HeapTupleIsValid(tuple))
+		{
+			attrtuple = (Form_pg_attribute) GETSTRUCT(tuple);
+			attrtuple->attstorage = newstorage;
+
+			CatalogTupleUpdate(attrelation, &tuple->t_self, tuple);
+
+			InvokeObjectPostAlterHook(RelationRelationId,
+									  RelationGetRelid(rel),
+									  attrtuple->attnum);
+
+			heap_freetuple(tuple);
+		}
+
+		index_close(indrel, lockmode);
+	}
+
 	heap_close(attrelation, RowExclusiveLock);
 
 	ObjectAddressSubSet(address, RelationRelationId,
diff --git a/src/test/regress/expected/alter_table.out b/src/test/regress/expected/alter_table.out
index a65f706deee..17b37708128 100644
--- a/src/test/regress/expected/alter_table.out
+++ b/src/test/regress/expected/alter_table.out
@@ -2255,6 +2255,26 @@ where oid = 'test_storage'::regclass;
  t
 (1 row)
 
+-- test that SET STORAGE propagates to index correctly
+create index test_storage_idx on test_storage (b, a);
+alter table test_storage alter column a set storage external;
+\d+ test_storage
+                                Table "public.test_storage"
+ Column |  Type   | Collation | Nullable | Default | Storage  | Stats target | Description 
+--------+---------+-----------+----------+---------+----------+--------------+-------------
+ a      | text    |           |          |         | external |              | 
+ b      | integer |           |          | 0       | plain    |              | 
+Indexes:
+    "test_storage_idx" btree (b, a)
+
+\d+ test_storage_idx
+                Index "public.test_storage_idx"
+ Column |  Type   | Key? | Definition | Storage  | Stats target 
+--------+---------+------+------------+----------+--------------
+ b      | integer | yes  | b          | plain    | 
+ a      | text    | yes  | a          | external | 
+btree, for table "public.test_storage"
+
 -- ALTER COLUMN TYPE with a check constraint and a child table (bug #13779)
 CREATE TABLE test_inh_check (a float check (a > 10.2), b float);
 CREATE TABLE test_inh_check_child() INHERITS(test_inh_check);
diff --git a/src/test/regress/sql/alter_table.sql b/src/test/regress/sql/alter_table.sql
index 9cdb92670e0..b211a2b90b4 100644
--- a/src/test/regress/sql/alter_table.sql
+++ b/src/test/regress/sql/alter_table.sql
@@ -1503,6 +1503,12 @@ select reltoastrelid <> 0 as has_toast_table
 from pg_class
 where oid = 'test_storage'::regclass;
 
+-- test that SET STORAGE propagates to index correctly
+create index test_storage_idx on test_storage (b, a);
+alter table test_storage alter column a set storage external;
+\d+ test_storage
+\d+ test_storage_idx
+
 -- ALTER COLUMN TYPE with a check constraint and a child table (bug #13779)
 CREATE TABLE test_inh_check (a float check (a > 10.2), b float);
 CREATE TABLE test_inh_check_child() INHERITS(test_inh_check);