Nowadays, multimedia systems are evolving towards integrated storage platforms that meet the requirements of deterministic applications, multimedia systems, and traditional best-effort applications altogether These systems must incorporate a disk scheduling mechanism and a cache architecture that can handle the requirements of each kind of request while showing a good overall performance. In this paper a new interval caching strategy is proposed that includes several optimizations to the state of the art. This algorithm has been designed to become part of MUPIC (multipolicy integrated cache), a cache architecture designed to fit the requirements of an integrated storage system. This paper presents the mathematical enunciation that led us to deploy new interval caching strategies and an evaluation of the algorithm proposed using a simulation program that compares it with other algorithms described in the bibliography. As shown in the conclusions MUPIC behaves the same or better in all the situations while providing admission control.