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Variable-bit-rate (VBR) compressed video can exhibit significant multiple-time-scale bit-rate variability. In this paper we consider the transmission of stored video from a server to a client across a network, and explore how the client buffer space can be used most effectively toward reducing the variability of the transmitted bit rate. Two basic results are presented. First, we show how to achieve the greatest possible reduction in rate variability when sending stored video to a client with given buffer size. We formally establish the optimality of our approach and illustrate its performance over a set of long MPEG-1 encoded video traces. Second, we evaluate the impact of optimal smoothing on the network resources needed for video transport, under two network service models: deterministic guaranteed service (Chang 1994; Wrege et al. 1996) and renegotiated constant-bit-rate (RCBR) service (Grossglauser et al. 1997 …