In one aspect of the present description, at least one of the value of a prestage trigger and the value of the prestage amount, may be modified as a function of the drive speed of the storage drive from which the units of read data are prestaged into a cache memory. Thus, cache prestaging operations in accordance with another aspect of the present description may take into account storage devices of varying speeds and bandwidths for purposes of modifying a prestage trigger and the prestage amount. Still further, a cache prestaging operation in accordance with further aspects may decrease one or both of the prestage trigger and the prestage amount as a function of the drive speed in circumstances such as a cache miss which may have resulted from prestaged tracks being demoted before they are used. Conversely, a cache prestaging operation in accordance with another aspect may increase one or both of the prestage trigger and the prestage amount as a function of the drive speed in circumstances such as a cache miss which may have resulted from waiting for a stage to complete. In yet another aspect, the prestage trigger may not be limited by the prestage amount. Instead, the pre-stage trigger may be permitted to expand as conditions warrant it by prestaging additional tracks and thereby effectively increasing the potential range for the prestage trigger. Other features and aspects may be realized, depending upon the particular application.