Index: wp-includes/post-template.php
===================================================================
--- wp-includes/post-template.php	(revision 1996)
+++ wp-includes/post-template.php	(working copy)
@@ -427,7 +427,7 @@
 
 		$classes[] = 'page-id-' . $pageID;
 
-		if ( $wpdb->get_var( $wpdb->prepare("SELECT ID FROM $wpdb->posts WHERE post_parent = %d AND post_type = 'page' LIMIT 1", $pageID) ) )
+		if ( empty($wp_query->post->ancestors) )
 			$classes[] = 'page-parent';
 
 		if ( $wp_query->post->post_parent ) {