Custom meny walker

Hello there wordpress masters!

I’m trying to generate a custom menu and have been trying in quite many ways now and can’t get a nice solution.
I’ve read this article, wich is close to what i want to achieve; http://www.kriesi.at/archives/improve-your-wordpress-navigation-menu-output

But, it’s not really the way i want it…
All the sub-menus get the class “sub-menu”. I want the first level of children to have another class, like “big-sub-menu”. Something like this…

<ul class="MainMenu">
    <li class="MainMenuButton">
        Main Button 1
        <!-- If this menu item has children -->
        <ul class="big-sub-menu">
            <li>
                Sub button 1.1
                <!-- If this menu item has children -->
                <ul class="sub-menu">
                    <li>Sub-Sub button 1.1.1</li>
                    <li>Sub-Sub button 1.1.2</li>
                </ul>
            </li>
            <li>
                Sub button 1.2
                <!-- If this menu item has children -->
                <ul class="sub-menu">
                    <li>Sub-Sub button 1.2.1</li>
                </ul>
            </li>
            <li>
                Sub button 1.3
                <!-- No children, no sub menu -->
            </li>
        </ul>
    </li>
    <li class="MainMenuButton">
        Main Button 2
        <!-- If this menu item has children -->
        <ul class="big-sub-menu">
            <li>
                Sub button 2.1
                <!-- If this menu item has children -->
                <ul class="sub-menu">
                    <li>Sub-Sub button 2.1.1</li>
                </ul>
            </li>
            <li>
                Sub button 2.2
                <!-- No children, no sub menu -->
            </li>
        </ul>
    </li>
</ul>

The theme will actually just have a maximum for 3 levels of menus, but i don’t wanna loop and iterate this manually for three levels. Feels ugly. Better so learn right from the beginning.
Any ideas?