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Consider a backoff algorithm for medium access in wireless networks where a node chooses with probability 1-q to transmit right away and with probability q to transmit after CW slots, where CW is the maximum value of the contention window. We study a variation of the 802.11 protocol called XVBEB which uses the above backoff scheme and give a theoretical analysis of its saturation throughput. Simulation results show that the throughput of XVBEB is better than that of 802.11 for saturated CBR traffic. Furthermore, XVBEB also exhibits lower packet loss, delay and delay variation than 802.11 for both VBR and VoIP traffic for a variety of load conditions.