Recently proposed streaming protocols are able to deliver multimedia files on-demand with required server bandwidth that grows only logarithmically with the file request rate. The same efficiencies are achieved for network bandwidth if delivery is over a true broadcast channel. This paper considers the required network bandwidth for on-demand streaming over multicast delivery trees. We consider both simple canonical delivery trees, and more complex cases in which delivery trees are constructed using both existing and new algorithms for various randomly generated network topologies and client site locations. Results in the paper quantify the potential savings from use of multicast trees that are configured to minimize network bandwidth rather than the latency to the content server. Further, we show that it is possible to simultaneously achieve reasonably close to the minimum possible network and server, bandwidth usage with a practical on-demand streaming protocol.