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In this paper, we propose a consistent random backoff (CRB) scheme to reduce the channel access delay jitter in voice over wireless local area networks (VoWLANs). In the CRB scheme, a contention window (CW) size at each backoff stage is determined by hashing the session identifier and the talk spurt index. Therefore, all packets in the same talk spurt of a session have the same CW sizes if they are transmitted at the same backoff stage. Since a modulo-division operation with the identical maximum CW value is applied, fairness with the legacy backoff scheme (i.e., binary exponential backoff (BEB)) is also provided. Extensive simulation results demonstrate that the CRB scheme can reduce the channel access delay jitter by 54%.