In this paper we formally introduce the notion of a D-redundant disk system. The class of D-redundant systems includes the class of physically mirrored disks with D copies as well as the more recently introduced SR systems. We provide a very general lower bound on the average access time of any D-redundant system. Using the lower bound we show that that the SR systems of Yu et el. are within 15 percent of optimal performance. We also show how SR systems can be combined with anticipatory head movement policies (AHM) to provide systems which are optimal within 5 percent.