scrollable fixed div

I have a menu in a div on the side of the browser and I would like to keep it in the fixed position. However, the menu may exceed height of some screens and that would result inaccessible links. So I would like to make the menu scrollable in such a case. Unfortunately the combination

position: fixed;
overflow: auto; (or scroll)

doesn't really work. I.e. the scrollbar is faded out (immovable). Is there a way? Thanks in advance

EDIT

The menu is similar to the one to the right up on this page. Only a bit larger. If you open that page and decrease the height of your browser window, part of the menu remains inaccessible. That's what I want to avoid. And no, my solution doesn't work in IE, Chrome, Opera or Fir开发者_如何学编程efox.

Add these to your declarations:

top: 0;
bottom: 0; /* or height: 100%; */

You can replace the zeroes with larger values to add margins.