Summary: A recently proposed approach measures balance and specialization degrees as opposite key performance indicators in addition to the efficiency and effectiveness scores well known from data envelopment analysis (DEA). It has been integrated into the DEA methodology by formulating output-oriented models of CCR- and BCC-type and has successfully been applied to two case studies of a European pharmacy business as well as German business schools’ research performance. Because the models are of (non-linear) minimax-type the calculation of the scores is not straightforward. Therefore this paper analyses the properties of the models in order to better understand them and to improve the solution process. The properties derived allow to propose an efficient heuristic solution procedure. While some properties hold for more general models others are true only for models with special convex polyhedric cones defining the balance set. A main result states that specialization of a decision-making unit is essentially measured by its angle distance to the balance cone.