The efficient transmission of constant quality compressed video streams is complicated by the burstiness (both short term and long term) that video compression standards such as MPEG introduce. Most of the techniques in the literature are concentrated on stored video traffic smoothing or real-time video traffic smoothing. However there is a growing number of live video applications, such as videocasts of courses or television news, where many clients may be willing to tolerate a playback delay of several seconds or minutes in exchange for a smaller throughput requirement. Bandwidth smoothing for these live video applications is referred to as online smoothing. In order to measure the effectiveness of online video smoothing methods, in this paper, we first propose a benchmark algorithm which provides the upper bound on some of the smoothness parameters in the smoothing results. Based on this algorithm, we found that significant discrepancy exists between the results produced by the existing online smoothing methods and the upper bound. With this observation, we then focus on devising algorithms which improve the smoothing results.