Bounded index exponential hashing, a new form of extendible hashing, is described. It has the important advantages over most of the other extendible hashing variants of both (i) providing random access to any record of a file in close to one disk access and (ii) having performance which does not vary with file size. It is straightforward to implement and demands only a fixed and specifiable amount of main storage to achieve this performance. Its underlying physical disk storage is readily managed and record overflow is handled so as to insure that unsuccessful searches never take more than two accesses. The method's ability to access data in close to a single disk access makes it possible to organize a database, in which files have a primary key and multiple secondary keys, such that the result is a significant performance advantage over existing organizations.