Fixed width horizontal menu with dropdown not showing.

I have a horizontal menu with a fixed width of 940px, with dropdown menus on each list item.

Since I want to limit the width to 940px and limit it to one row of items, I put overflow: hidden in the parent container of the horizontal menu. However, this now hides all of the dropdown menus in my list.

How do I make it so that I can cut off the horizontal menu items if they exceed the width of 940px, but still keep the dropdown items? I’ve been trying to search everywhere for this, but can’t find an example where people will limit their menu to a certain width and height.

I’ve swiped an example from psdgraphics.com and uploaded it to show you what I mean.

http://jsfiddle.net/tcKvH/98/

TLDR: I put an overflow:hidden in the parent div to clip horizontal list items so the menu doesn’t grow past a certain width or break up into several rows. But now my dropdown submenus won’t show.

If anyone can help, or point to a working example/theme that does this, that would be appreciated.