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The contention resolution scheme is a key component in carrier-sense-based wireless MAC protocols. It has a major impact on MAC'S performance metrics such as throughput, delay, and jitter. The IEEE 802.11 DCF adopts a simple contention resolution scheme, namely, the binary exponential backoff (BEB) scheme. The BEB scheme achieves a reasonable performance for transmitting best-effort packets in small-sized wireless networks. However, as the network size increases, it suffers from inefficiency because of the medium contention, which leads to reduced performance. The main reason is that the BEB mechanism incurs an ever- increasing collision rate as the number of contending nodes increases. We devise a novel contention resolution scheme, a k-round elimination contention (k-EC) scheme. The k-EC scheme exhibits high efficiency and robustness during the collision resolution. More importantly, it is insensitive to the number of contending nodes. This feature makes it feasible for use in networks of different sizes. Simulation results show that the k-EC scheme offers a powerful remedy to medium contention resolution. It significantly outperforms the IEEE 802.11 DCF scheme in all the MAC'S performance metrics and also exhibits better fairness.