Index: contextual.module
===================================================================
--- contextual.module
+++ contextual.module
@@ -88,6 +88,17 @@
         'query' => array('destination' => $_GET['q']),
       );
     }
+    if ($object->module == 'menu' && user_access('administer menu')) {
+      $links['menu-configure'] = array(
+        'title' => t('Customize menu'),
+        'href' => "admin/build/menu-customize/{$object->delta}",
+        'attributes' => array('class' => 'icon-edit'),
+        'query' => array('destination' => $_GET['q']),
+      );
+
+      // Change the menu configure link to avoid confusion.
+      $links['block-configure']['title'] = t('Configure block');
+    }
   }
   return $links;
 }