AbstractData Envelopment Analysis (DEA) is an approach to assess the relative efficiency of organizations using multiple inputs to produce multiple outputs. This assessment is made from the standpoint most favourable to each organization. If an organization is not well enveloped, in the sense that it is not comparable to a sufficient number of other organizations (called referents), DEA may understate inefficiency. A lower bound on the efficiency measure may be obtained by requiring that the organization being evaluated be compared with at leastknon-redundant referents. For any feasible choice ofk, the procedure proposed here selects the most favourable set of referents, and guarantees a greatest lower bound on the efficiency measure, thus usefully complementing the information provided by conventional DEA.