Request for help with wp_list_categories

Dear fellow WordPress users,

I’d be very grateful if someone could help me out with the following problem. Thanks very much indeed.

——————————-

I am using wp_list_categories to show the categories but I want them
formatted in a certain way as shown below.
The odd/even class and the spans are important as I want an alternating

background color.

<ul>

<li class="odd"><span><a href="" title="">Parent category</a>
<ul class="clearfix">
<li><a href="" title="">Child category</a></li>
<li><a href="" title="">Child category</a></li>
</ul>
</span></li>

<li><span><a href="" title="">Parent category</a>
<ul class="clearfix">
<li><a href="" title="">Child category</a></li>
<li><a href="" title="">Child category</a></li>
</ul>
</span></li>

</ul>

Any way I can go about this? (As a last resort, is this possible by
hacking the “category-template” file?)