Streaming variable-bit-rate video over wide-area networks has many challenging problems due to the great variation of network conditions. In this paper, we focus on the problem of the efficient utilization of the precious network bandwidth in such streaming systems. We propose a novel piggyback prefetching mechanism to improve the bandwidth utilization. We achieve this goal by making use of the unoccupied bandwidth in ongoing streams to deliver some prefetched data and use them to serve future requests. This idea can be applied in various different ways to improve bandwidth utilization. Experimental results show that our mechanism not only can improve bandwidth utilization significantly, but also it can improve the caching performance of the proxy servers in the streaming systems.