The tape mount optimization for data set recoveries is accomplished by recovering all queued or soon arriving data set requests from a single and common backup tape with a single tape mount. For media before 3480s, those requests from a single and common backup tape are processed in ascending file-block ID. For 3480 (single-file-format tape cartridges) and later media, those requests from a single and common backup tape are processed in priority order on the recovery queue. The tape mount optimization is not applied to data set requests from dump tapes or when a data set spans backup tapes.