1px borders doubling up, any workaround/fix?

I'd really appreciate any help with this css problem, I've spent hours trying to figure it out but I'm stumped.

I'm working on a CSS pop-out menu, and the problem I'm having is this:

I want a 1px border around each menu and submenu item, but in every place an item is touching another, the 1px borders obviously show up twice and then it looks like a 2px border.

Right now I've got it to work and validate, by giving everything a top & right border, and filling in the other ones manually. But it takes quite a lot of extra code for something so small.
I've assigned each list item which needs a border a class, then created a stylesheet rule for that class. Is there a better way?

I've run into another problem too, the menu items which have a submenu need to have a little arrow on the right hand side. Right now I've got that on there with a <span>, but I can't seem to position it. I can't give the list item a class, and set that as the background because it already has a class.

the page is here: http://wolfe.rchomepage.com
and the css is here: http://wolfe.rchomepage.com/menuv.css

a picture of what I'm trying to achieve is here: http://wolfe.rchomepage.com/menu.jpg

I want a 1px border around each menu and submenu item, but in every place an item is touching another, the 1px borders obviously show up twice and then it looks like a 2px border.
Looks like you have fixed this problem. I don't see the 2px borders?
I can't give the list item a class, and set that as the background because it already has a class.
You can give an element multiple classes like this:

<li class="monkey zebra giraf">...</li>

(1)
As a side issue, I would remove this:

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
It is causing your page to be rendered in quirks mode (http://www.quirksmode.org/css/quirksmode.html) in IE6.

For what reason are you even using XHTML? Read what Arbitrator has to say about using XHTML for web pages: http://codingforums.com/showpost.php?p=569539&postcount=9

(2)
Looks like you haven't finished the menu for IE6 functionality?