MPEG video transmission will make up a significant portion of the workload on future computer networks. These variable bit rate (VBR) compressed video is known to exhibit significant, multiple time scale bit rate variability. To such bursty traffic, it is always a compromise between providing a good quality of service (QoS) and a high utilization on the network bandwidth. One can adopt an optimal video smoothing algorithm (J. Salchi et al., 1996) to smooth out the data transmission from a server to a client so that the network utilization can be improved. We present a smoothing algorithm for transmitting stored MPEG-1 video stream under a user defined maximum network bandwidth. We also consider the impact of the startup latency, and the client's buffer size on the network utilization. Our algorithm differs from the others in that we do video smoothing under a predefined bandwidth. At the cost of either deleting B-frames for a short period of time or by introducing a one-time playback pause, the network utilization can be improved dramatically without sacrificing much on the video quality.