The task of supporting integrated multirate multimedia traffic in a bandwidth-poor wireless environment poses a significant challenge for network designers. In this paper we propose a novel bandwidth allocation strategy which partitions the available bandwidth amongst the different traffic classes in a manner that ensures quality-of-service guarantees for digital ideo while minimizing the maximum blocking probability for voice and data connections. At the connection level, near-optimum utilization of the reserved bandwidth for video traffic is achieved through an intra-frame statistical multiplexing algorithm, while at the system level the delicate task of partitioning the bandwidth between voice, video and data is accomplished by developing an efficient algorithm which uses traffic parameters consisting only of the aggregate traffic load and the total available bandwidth. The algorithm, built on non-trivial mathematical results is robust, easy to implement and has a geometric rate of convergence which ensures that the partitioning points are found quickly. These properties make it well suited for practical implementations, even for cases where changes in the aggregate traffic loads cause bandwidth allocations to be recomputed frequently.