diff -urN superfish.orig/superfish.module superfish/superfish.module
--- superfish.orig/superfish.module	2010-12-28 22:17:28.000000000 +0200
+++ superfish/superfish.module	2010-12-28 22:14:51.000000000 +0200
@@ -557,7 +557,7 @@
         $output .= '>'. $lw[0] . theme('menu_item_link', $menu_item['link']) . $lw[1];
         if ($menu_item['link']['depth'] <= $depth || $depth == -1) {
           if ($children) {
-            $output .= "\n<ul>\n". $children ."</ul>\n";
+            $output .= "\n<ul style='display: none;'>\n". $children ."</ul>\n";
           }
         }
         $output .= "</li>\n";