A data storage apparatus has a plurality p of storage spaces for storing sets of data. Each of the spaces has: available (unused) space x.sub.1 for storage; a number x.sub.2 of data sets already stored; a number x.sub.3 of channels available for transferring data to the space; and a number x.sub.4 of times the space is scheduled to be used for reading out sets of data therefrom. An allocation factor Qp=f(ai, xi) is calculated for each space where ai are weighting factors ranking xi in order of importance. A data set is allocated to the space having the "best" (e.g. lowest) value of Qp at the time the data is to be allocated. Once allocation factors determined, then data may be allocated according to usage indices representing the ability of a space to store the data at the time of allocation.