diff --git a/src/wp-includes/query.php b/src/wp-includes/query.php
index cf7b80f772..971e75ffcb 100644
--- a/src/wp-includes/query.php
+++ b/src/wp-includes/query.php
@@ -4311,7 +4311,7 @@ class WP_Query {
 	 *
 	 * @since 3.1.0
 	 *
-	 * @param mixed $page Page ID, title, slug, or array of such.
+	 * @param mixed $page Page ID, title, slug, path, or array of such.
 	 * @return bool
 	 */
 	public function is_page( $page = '' ) {
@@ -4325,12 +4325,24 @@ class WP_Query {
 
 		$page = (array) $page;
 
-		if ( in_array( $page_obj->ID, $page ) )
+		if ( in_array( $page_obj->ID, $page ) ) {
 			return true;
-		elseif ( in_array( $page_obj->post_title, $page ) )
+		} elseif ( in_array( $page_obj->post_title, $page ) ) {
 			return true;
-		else if ( in_array( $page_obj->post_name, $page ) )
+		} else if ( in_array( $page_obj->post_name, $page ) ) {
 			return true;
+		} else {
+			foreach ( $page as $pagepath ) {
+				if ( ! strpos( $pagepath, '/' ) ) {
+					continue;
+				}
+				$pagepath_obj = get_page_by_path( $pagepath );
+
+				if ( $pagepath_obj && ( $pagepath_obj->ID == $page_obj->ID ) ) {
+					return true;
+				}
+			}
+		}
 
 		return false;
 	}
@@ -4392,7 +4404,7 @@ class WP_Query {
 	 *
 	 * @since 3.1.0
 	 *
-	 * @param mixed $post Post ID, title, slug, or array of such.
+	 * @param mixed $post Post ID, title, slug, path, or array of such.
 	 * @return bool
 	 */
 	public function is_single( $post = '' ) {
@@ -4406,13 +4418,24 @@ class WP_Query {
 
 		$post = (array) $post;
 
-		if ( in_array( $post_obj->ID, $post ) )
+		if ( in_array( $post_obj->ID, $post ) ) {
 			return true;
-		elseif ( in_array( $post_obj->post_title, $post ) )
+		} elseif ( in_array( $post_obj->post_title, $post ) ) {
 			return true;
-		elseif ( in_array( $post_obj->post_name, $post ) )
+		} elseif ( in_array( $post_obj->post_name, $post ) ) {
 			return true;
+		} else {
+			foreach ( $post as $postpath ) {
+				if ( ! strpos( $postpath, '/' ) ) {
+					continue;
+				}
+				$postpath_obj = get_page_by_path( $postpath, OBJECT, $post_obj->post_type );
 
+				if ( $postpath_obj && ( $postpath_obj->ID == $post_obj->ID ) ) {
+					return true;
+				}
+			}
+		}
 		return false;
 	}
 
diff --git a/tests/phpunit/tests/query/conditionals.php b/tests/phpunit/tests/query/conditionals.php
index 1af50ac7aa..0f0931b385 100644
--- a/tests/phpunit/tests/query/conditionals.php
+++ b/tests/phpunit/tests/query/conditionals.php
@@ -692,6 +692,53 @@ class Tests_Query_Conditionals extends WP_UnitTestCase {
 		$this->assertTrue( is_single( $post->post_name ) );
 	}
 
+	/**
+	 * @ticket 16802
+	 */
+	function test_is_single_with_parent() {
+		// Use custom hierarchical post type
+		$post_type = 'test_hierarchical';
+
+		register_post_type( $post_type, array(
+			'hierarchical' => true,
+			'rewrite'      => true,
+			'has_archive'  => true,
+			'public'       => true
+		) );
+
+		// Create parent and child posts
+		$parent_id = $this->factory->post->create( array(
+			'post_type' => $post_type,
+			'post_name' => 'foo'
+		) );
+
+		$post_id = $this->factory->post->create( array(
+			'post_type'   => $post_type,
+			'post_name'   => 'bar',
+			'post_parent' => $parent_id
+		) );
+
+		// Tests
+		$this->go_to( "/?p=$post_id&post_type=$post_type" );
+
+		$post = get_queried_object();
+		$q = $GLOBALS['wp_query'];
+
+		$this->assertTrue( is_single() );
+		$this->assertFalse( $q->is_page );
+		$this->assertTrue( $q->is_single );
+		$this->assertFalse( $q->is_attachment );
+		$this->assertTrue( is_single( $post ) );
+		$this->assertTrue( is_single( $post->ID ) );
+		$this->assertTrue( is_single( $post->post_title ) );
+		$this->assertTrue( is_single( $post->post_name ) );
+		$this->assertTrue( is_single( 'foo/bar' ) );
+		$this->assertFalse( is_single( $parent_id ) );
+		$this->assertFalse( is_single( 'foo/bar/baz' ) );
+		$this->assertFalse( is_single( 'bar/bar' ) );
+		$this->assertFalse( is_single( 'foo' ) );
+	}
+
 	function test_is_page() {
 		$post_id = $this->factory->post->create( array( 'post_type' => 'page' ) );
 		$this->go_to( "/?page_id=$post_id" );
@@ -709,6 +756,39 @@ class Tests_Query_Conditionals extends WP_UnitTestCase {
 		$this->assertTrue( is_page( $post->post_name ) );
 	}
 
+	/**
+	 * @ticket 16802
+	 */
+	function test_is_page_with_parent() {
+		$parent_id = $this->factory->post->create( array(
+			'post_type' => 'page',
+			'post_name' => 'foo',
+		) );
+		$post_id = $this->factory->post->create( array(
+			'post_type'   => 'page',
+			'post_name'   => 'bar',
+			'post_parent' => $parent_id,
+		) );
+		$this->go_to( "/?page_id=$post_id" );
+
+		$post = get_queried_object();
+		$q = $GLOBALS['wp_query'];
+
+		$this->assertTrue( is_page() );
+		$this->assertFalse( $q->is_single );
+		$this->assertTrue( $q->is_page );
+		$this->assertFalse( $q->is_attachment );
+		$this->assertTrue( is_page( $post ) );
+		$this->assertTrue( is_page( $post->ID ) );
+		$this->assertTrue( is_page( $post->post_title ) );
+		$this->assertTrue( is_page( $post->post_name ) );
+		$this->assertTrue( is_page( 'foo/bar' ) );
+		$this->assertFalse( is_page( $parent_id ) );
+		$this->assertFalse( is_page( 'foo/bar/baz' ) );
+		$this->assertFalse( is_page( 'bar/bar' ) );
+		$this->assertFalse( is_page( 'foo' ) );
+	}
+
 	function test_is_attachment() {
 		$post_id = $this->factory->post->create( array( 'post_type' => 'attachment' ) );
 		$this->go_to( "/?attachment_id=$post_id" );