A peer-assisted content delivery system uses the upload bandwidth of its clients to assist in delivery of popular content. In peer-assisted systems using a BitTorrent-like protocol, a content delivery server seeds the offered files, and active torrents form when multiple clients make closely-spaced requests for the same content. Scalability is achieved in the sense of being able to accommodate arbitrarily high request rates for individual files. Scalability with respect to the number of files, however, may be much more difficult to achieve, owing to a "long tail" of lukewarm or cold files for which the server may need to assume most or all of the delivery cost. This paper first addresses the question of how best to allocate server resources among multiple active torrents. We then propose new content delivery policies that use some of the available upload bandwidth from currently downloading clients to "inflate" torrents for files that would otherwise require substantial server bandwidth. Our performance results show that use of torrent inflation can substantially reduce download times, by more than 50% in some cases.