Most multimedia applications require storage and retrieval of large amounts of continuous and discrete data at very high rates. Disk drives should be servicing such mixed workloads achieving low response times for discrete requests, while guaranteeing the uninterrupted delivery of continuous data. Disk scheduling algorithms for mixed workloads, although they play a central role in this task, have been overlooked by related multimedia research efforts, which so far have mostly concentrated on the scheduling of continuous requests only. The focus of this paper is on efficient disk I/O scheduling algorithms for mixed workloads in a multimedia storage server. We propose novel algorithms, a taxonomy of relevant algorithms, and study their performance through experimentation. Our results show that our proposed algorithms offer drastic improvements in discrete request average response times, low response-time variability, while serving continuous requests without interruptions.