Since the back-off windows among competing users are not synchronized, the binary exponential back-off (BEB) algorithm results in a "capture effect" and, in the limit as the number of users approaches infinity, BEB is unstable for every arrival rate greater than 0. Both fixed collision rate (FCR) and quasi-FIFO algorithms have been proposed for collision resolution in wireless networks to remedy the drawbacks in BEB. A novel virtually-FIFO back-off algorithm is introduced to improve further the throughput and fairness in bandwidth utilization. In the virtually-FIFO scheme, packets generated in a given cycle period are guaranteed to be serviced within the next cycle and the order of services is virtually based on their times of arrival. With the virtually-FIFO scheme, the standard deviation of delay in BEB can be improved by more than two orders of magnitude and throughput is maintained at above 0.422.