We consider designing near video on demand (VoD) systems that minimize start-up latency while maintaining high image quality. Recently non-uniform segmentation has been used to develop periodic broadcasting techniques for near VoD. These techniques give significant reductions in start-up latency as compared with more conventional uniform segmentation. All of these schemes assume, however, that the videos are CBR-encoded. Since a CBR-encoded video has a larger average rate than an open-loop VBR encoding with the same image quality, there is potential to obtain further performance improvements by using VBR video. In this paper we develop a series of multiplexing schemes for the periodic broadcasting of VBR-encoded video, which are based on smoothing, server buffering and client prefetching. Two key but coflicting performance measures exist when using VBR video: latency and packet loss. By introducing small additional delays in our multiplexing schemes, our traced-based numerical work shows that the schemes can achieve nearly 100% link utilization with negligible packet loss. When the ratio of the CBR rate to the VBR average rate is a modest 1.8, start-up latency can be reduced by a factor of four or more for common scenarios.