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This paper presents and evaluates a distributed mechanism for the contention control in IEEE 802.11 Wireless LANs. Specifically, our mechanism named Asymptotically Optimal Backoff (AOB), dynamically adapts the backoff window size to the current load. AOB guarantees that an IEEE 802.11 WLAN asymptotically (i.e. for a large number of active stations) achieves its optimal channel utilization. The proposed mechanism merges the ideas on adaptive backoff presented previously with some properties derived from the IEEE 802.11 capacity analysis. AOB can be used on top of the standard 802.11 access mechanism without requiring any modification to the standard or additional hardware. The AOB mechanism adapts the backoff to the network contention level by using two simple load estimates: the slot utilization and the average size of transmitted frames. These estimates are simple and can be obtained with no additional costs or overheads. The performance of the IEEE 802.11 protocol with or without the AOB mechanism is investigated in the paper via simulation. Simulative results indicate that our mechanism is very effective and brings the utilization of the system close to the optimal level for a wide range of load and network configurations.