altering menu links

I'm lost from the previous 4 hours looking for the right Drupal 6 code and/or how to implement it.
In short: I have a website. It has a menu. This menu is the Primary Links menu. I want to 'alter' each link that is displayed in this section to have tags enclosed around the link text. These span tags should be inside the tags.
Rather than this:

  • Test
  • It should look like:

  • Test
  • ...and I'm using the following to output the menu:
    <?php print menu_tree($menu_name = 'primary-links');?>
    I have checked out menu_tree, menu_tree_item API specifically (I assumed that's what I needed) but can't really get anything set in stone. I also took a look at hook_menu_link_alter, but I don't think that is going to do what I want to do.
    I don't know now; I've read enough to be confused. I can't ever tell if I'm reading code for D4, D5, or D6 (Other than the 'posted' date)
    If someone could point me in the right direction, that would be awesome!

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