VBR compressed video is known to 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 high speed network, and explore how the client buffer space can be used most effectively toward reducing the variability of the transmitted bit rate. We present two basic results. First, we present an optimal smoothing algorithm for achieving the greatest possible reduction in rate variability when transmitting stored video to a client with given buffer size. We provide a formal proof of optimality, and demonstrate the performance of the algorithm on 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 [1, 9] and Renegotiated CBR (RCBR) service [8, 7]. Under both models, we find the impact of optimal smoothing to be dramatic.