Variable bit-rate (VBR) compressed video traffic is expected to be a significant component of the traffic mix in integrated services networks. This traffic is hard to manage because it has strict delay and loss requirements while simultaneously exhibiting burstiness at multiple time scales. We show that burstiness over long time scales, in conjunction with resource reservation using one-shot traffic descriptors, can substantially degrade the loss rate, end-to-end delay, and statistical multiplexing gain of a connection. We use large-deviation theory to model the performance of multiple time-scale traffic and to motivate the design of renegotiated constant bit rate (RCBR) service. Sources using RCBR service are presented with an abstraction of a fixed-size buffer which is drained at a constant rate. They may renegotiate the drain rate to match their workload. Because all traffic entering the network is constant bit-rate (CBR), RCBR requires minimal buffering and scheduling support in switches. We show that the service is suitable for both stored and online video sources. An RCBR source must decide when to renegotiate its service rate and what the new service rate should be. We present: (1) an algorithm to compute the optimal renegotiation schedule for stored (offline) traffic and (2) a heuristic to approximate the optimal schedule for online traffic. We also discuss measurement-based admission control (MBAC) for RCBR traffic. Simulation experiments show that RCBR is able to extract almost all of the statistical multiplexing gain available by exploiting slow time-scale variations in traffic. Moreover, simple admission control schemes are sufficient to keep the renegotiation failure probability below a small threshold while still offering high link utilization. Thus, we believe that RCBR is a simple, practical, and effective service for carrying multiple time-scale traffic.