In a hierarchical storage management system (HSM), a scheduled-recall request is associated with a start-time. Prior to the scheduled-recall request start-time, if a first recall request is directed to the same storage medium as is the scheduled-recall request, the method performs some or all of the scheduled-recall request, with low priority processing, during times that the storage drive (performing the first recall request) is otherwise idle. After the scheduled-recall request start-time, the priority of the scheduled-recall request is increased and data targeted by the scheduled-recall request, that had not already been recalled during the low priority processing, are subsequently processed with high priority.