Abstract: We present a fast and energy-efficient z-comparator that takes advantage of the fact that the result of most depth comparisons can be determined by examining just a few bits. This feature is made possible by the use of asynchronous logic, which enables the comparator to rapidly compare bits until the result is clear and then stop. Using depth data from well-known computer games, SPICE simulations indicate that our comparator consumes only 25% of the energy and operates 1.67 times faster, on average, compared to an equivalent synchronous design. The comparator design is used to illustrate a more general design principle, "compute on demand," which can potentially enable graphics hardware to be faster and more energy-efficient.