How can I make the contents of a fixed element scrollable only when it exceeds the height of the viewport?

You probably can’t. Here’s something that comes close. You won’t get content to flow around it if there’s space below.

http://jsfiddle.net/ThnLk/1289

.stuck {
    position: fixed;
    top: 10px;
    left: 10px;
    bottom: 10px;
    width: 180px;
    overflow-y: scroll;
}

You can do a percentage height as well:

http://jsfiddle.net/ThnLk/1287/

.stuck {
    max-height: 100%;
}