Index: wp-includes/theme.php
===================================================================
--- wp-includes/theme.php	(revision 25119)
+++ wp-includes/theme.php	(working copy)
@@ -1034,12 +1034,15 @@
  *
  * @since 3.4.0
  *
- * @return object
+ * @return mixed False if there is no header, or an object with the properties
+ * 	'url', 'thumbnail_url', 'width', and 'height'.
  */
 function get_custom_header() {
 	global $_wp_default_headers;
 
-	if ( is_random_header_image() ) {
+	if ( 'remove-header' == get_theme_mod( 'header_image' ) ) {
+		return false;
+	} elseif ( is_random_header_image() ) {
 		$data = _get_random_header_data();
 	} else {
 		$data = get_theme_mod( 'header_image_data' );