Aiming at the efficient retrieval of objects with set-valued attributes, we introduce three variations of a new method in order to satisfy subset and superset queries. Our approach is to combine the advantages of two access methods, that of linear Hashing and of tree-shaped methods, on which other similar methods have been previously reported as well. Performance estimation analytical functions for each particular method are presented, followed by a thorough experimental comparison of all investigated structures, where analytical and experimental results deviate 10% on the average. Finally, the results of this performance evaluation are presented and discussed, clearly showing the superiority of the new methods reaching an improvement of up to 85%. r