Advanced input queuing is an attractive, promising architecture for high-speed ATM switches, because it combines the low cost of input queuing with the high performance of output queuing. The need for scalable schedulers for advanced input queuing switch architectures has led to the development of efficient distributed scheduling algorithms. We introduce a new distributed scheduling algorithm, FIRM, which provides improved performance characteristics over alternative distributed algorithms. FIRM achieves saturation throughput 1 with lower delay than the most efficient alternative (up to 50% at high load). Furthermore, it provides improved fairness (it approximates FCFS) and tighter service guarantee than others. FIRM provides a basis for a class of distributed scheduling algorithms, many of which provide even more improved performance characteristics.