diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index 0cb91afada..1b53e0b03b 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -5405,14 +5405,10 @@ ATSimpleRecursion(List **wqueue, Relation rel,
 				  AlterTableCmd *cmd, bool recurse, LOCKMODE lockmode)
 {
 	/*
-	 * Propagate to children if desired.  Only plain tables, foreign tables
-	 * and partitioned tables have children, so no need to search for other
-	 * relkinds.
+	 * Propagate to children, if desired and if there are (or might be) any
+	 * children.
 	 */
-	if (recurse &&
-		(rel->rd_rel->relkind == RELKIND_RELATION ||
-		 rel->rd_rel->relkind == RELKIND_FOREIGN_TABLE ||
-		 rel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE))
+	if (recurse && rel->rd_rel->relhassubclass)
 	{
 		Oid			relid = RelationGetRelid(rel);
 		ListCell   *child;
@@ -6386,6 +6382,41 @@ ATPrepSetNotNull(List **wqueue, Relation rel,
 	if (recursing)
 		return;
 
+	/*
+	 * If the target column is already marked NOT NULL, we can skip recursing
+	 * to children, because their columns should already be marked NOT NULL as
+	 * well.  But there's no point in checking here unless the relation has
+	 * some children; else we can just wait till execution to check.  (If it
+	 * does have children, however, this can save taking per-child locks
+	 * unnecessarily.  This greatly improves concurrency in some parallel
+	 * restore scenarios.)
+	 *
+	 * Unfortunately, we can only apply this optimization to partitioned
+	 * tables, because traditional inheritance doesn't enforce that child
+	 * columns be NOT NULL when their parent is.  (That's a bug that should
+	 * get fixed someday.)
+	 */
+	if (rel->rd_rel->relhassubclass &&
+		rel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
+	{
+		HeapTuple	tuple;
+		bool		attnotnull;
+
+		tuple = SearchSysCacheAttName(RelationGetRelid(rel), cmd->name);
+
+		/* Might as well throw the error now, if name is bad */
+		if (!HeapTupleIsValid(tuple))
+			ereport(ERROR,
+					(errcode(ERRCODE_UNDEFINED_COLUMN),
+					 errmsg("column \"%s\" of relation \"%s\" does not exist",
+							cmd->name, RelationGetRelationName(rel))));
+
+		attnotnull = ((Form_pg_attribute) GETSTRUCT(tuple))->attnotnull;
+		ReleaseSysCache(tuple);
+		if (attnotnull)
+			return;
+	}
+
 	/*
 	 * If we have ALTER TABLE ONLY ... SET NOT NULL on a partitioned table,
 	 * apply ALTER TABLE ... CHECK NOT NULL to every child.  Otherwise, use