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The IEEE 802.15.4 standard utilizes the Binary Exponential Backoff (BEB) algorithm to control nodes' access to the shared wireless medium. The main drawback of BEB is that it updates the size of the contention window (CW) without taking into consideration the number of competing nodes and the conditions in the communications medium. Therefore, BEB has been shown to be inefficient in terms of channel utilization and fairness among the contending nodes. In this paper, we propose Adaptive Backoff Algorithm (ABA), a new backoff algorithm that adaptively determines the appropriate size of CW based on the collisions experienced by the nodes. That is, while BEB updates CW in a deterministic fashion, we introduce a probabilistic methodology to achieve that update. Our simulations compare the performance of ABA with that of BEB as well as three other algorithms proposed in the literature, namely, NO-BEB, KEB, and IBEB. The performance is studied in terms of power consumption, reliability, and channel utilization. Our results show that ABA outperforms the aforementioned algorithms while granting each node a fair access to the wireless medium.