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In this paper, we explore, via an extensive simulation study, the performance of a call-admission-control (CAC) and traffic-policing mechanisms proposed for transmitting multiple quality encoded videoconference movies over a wireless asynchronous transfer mode channel of high capacity, depending on the user's needs and requests. Both the CAC algorithm and the traffic-policing mechanism are novel mechanisms proposed for the first time in this paper. For their implementation, we use an estimation of the equivalent bandwidth of the movies, which has been introduced in the past. We focus on both MPEG-4 and H.263 coded movies, as the integration of such video streams has not been studied in the relevant literature. In the case of H.263 movies, our scheme achieves high aggregate channel throughput, while preserving the very strict quality-of-service requirements of the video traffic.