This paper presents an adaptive backoff algorithm for the contention-based Distributed Coordination Function (DCF) of the IEEE 802.11 standard. Relying on on-line measurements of the number of sources, the algorithm, called Adaptive BEB, judiciously sets the size of the minimal contention window to adapt to the congestion level in the shared medium. The paper also provides an extension to Adaptive BEB for enhancing its performance over noisy channels. In this extension, a simple EWMA filter is used to derive a Packet Error Rate estimator. The performance evaluation of our proposal is addressed via simulations.