Mozilla correctly handles image maps that are not XHTML-compliant. The following works in Mozilla...
In this case, hovering over each of the two options shows a different alt description, and clicking on Link 1 takes you to my other example.
The only real difference here is that I've used <map name="links"> instead of the XHTML-compliant version, <map id="links">, making this page and the image map invalid XHTML.