A multimedia server delivers presentations (such as videos, movies, games), providing high bandwidth and continuous real-time delivery. In this paper we present techniques for reducing the initial latency of presentations, that is, for reducing the time between the arrival of a request and the start of the presentation. Traditionally, initial latency has not received much attention. This is because one major application of multimedia servers is ``movies on demand'' where a delay of a few minutes before a new multi-hour movie starts is acceptable. However, latency reduction becomes important in interactive applications such as video games and browsing multimedia documents. Various latency reduction schemes are examined and proposed, and their performance compared. Analysis shows that on-disk partial data replication technique can significantly reduce (almost eliminate in some cases) initial latency without adversely affecting throughput. The on-disk partial data replication scheme that we propose proves far more cost effective than any previous attempts to reduce initial latency.