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This paper considers a fairness issue between uplink and downlink flows in IEEE 802.11 wireless LANs, where uplink flows dominate over downlink flows in terms of wireless bandwidth usage. As a solution to this unfairness, we propose modifying the IEEE 802.11 MAC protocol at access points (APs). Our scheme dynamically controls the minimum contention window size at APs and provides an ample opportunity for them to acquire the transmission right. Note that the proposed scheme does not require any modifications in the MAC protocol at wireless terminals. Furthermore, the optimal minimum contention window size is given by an explicit function of the ratio of the total packet rate of downlink flows to the packet rate of an uplink flow. Through simulation experiments with UDP and TCP flows, we show that the proposed scheme can achieve fairness between uplink and downlink flows.