Modified tracks for write requests to a sequential access storage medium in a sequential access storage device are cached in a non-volatile storage, which is a faster access device than the sequential access storage medium. A request queue includes destage requests to destage the modified tracks in the non-volatile storage device to the sequential access storage medium and read requests to access read requested tracks from the sequential access storage medium. A comparison is made of a current position of a read/write mechanism with respect to physical locations on the sequential access storage medium of the tracks subject to the destage requests indicated in the request queue. A determination is made of one of the destage requests to process based on the comparison. The modified track for the determined destage request is written from the non-volatile storage device to the sequential access storage medium.