How do I change the ID of a HTML element with JavaScript?

I am modifying the ID of an HTML div element client side with JavaScript. The following code works OK in Internet Explorer but not in Firefox/2.0.0.20. It does work in more recent versions of Firefox.

document.getElementById('one').id = 'two';

Can anyone tell me:

1. Why this doesn't work in FireFox.
2. How to make this work in FireFox.

To clarify, I'm changing the element ID to reference a different style in an external style sheet. The style is applied in IE but not in FF.