wp_nav_menu() customized

In my basis theme I use a walker for a simplified output:

<?php # -*- coding: utf-8 -*-
/**
 * Create a nav menu with very basic markup.
 *
 */
class T5_Nav_Menu_Walker_Simple extends Walker_Nav_Menu
{
    /**
     * Start the element output.
     *
     * @param  string $output Passed by reference. Used to append additional content.
     * @param  object $item   Menu item data object.
     * @param  int $depth     Depth of menu item. May be used for padding.
     * @param  array $args    Additional strings.
     * @return void
     */
    public function start_el( &$output, $item, $depth, $args )
    {
        $output     .= '<li>';
        $attributes="";

        ! empty ( $item->attr_title )
            // Avoid redundant titles
            and $item->attr_title !== $item->title
            and $attributes .= ' title="' . esc_attr( $item->attr_title ) .'"';

        ! empty ( $item->url )
            and $attributes .= ' href="' . esc_attr( $item->url ) .'"';

        $attributes  = trim( $attributes );
        $title       = apply_filters( 'the_title', $item->title, $item->ID );
        $item_output = "$args->before<a $attributes>$args->link_before$title</a>"
                        . "$args->link_after$args->after";

        // Since $output is called by reference we don't need to return anything.
        $output .= apply_filters(
            'walker_nav_menu_start_el'
            ,   $item_output
            ,   $item
            ,   $depth
            ,   $args
        );
    }

    /**
     * @see Walker::start_lvl()
     *
     * @param string $output Passed by reference. Used to append additional content.
     * @return void
     */
    public function start_lvl( &$output )
    {
        $output .= '<ul class="sub-menu">';
    }

    /**
     * @see Walker::end_lvl()
     *
     * @param string $output Passed by reference. Used to append additional content.
     * @return void
     */
    public function end_lvl( &$output )
    {
        $output .= '</ul>';
    }

    /**
     * @see Walker::end_el()
     *
     * @param string $output Passed by reference. Used to append additional content.
     * @return void
     */
    function end_el( &$output )
    {
        $output .= '</li>';
    }
}

See this answer for implementation details.