The idea is to find out whether 2nd law efficiency optimization may be a suitable trade-off between maximum work output and maximum 1st law efficiency designs for a regenerative gas turbine engine operating on the basis of an open Brayton cycle. The primary emphasis is placed on analyzing the ideal cycle to determine the upper limit of the engine. Explicit relationships are established for work and entropy production of the ideal cycle. To examine whether a Brayton cycle may operate at the regime of fully reversible characterized by zero entropy generation condition, the cycle net work is computed. It is shown that an ideal Brayton-type engine with or without a regenerator cannot operate at fully reversible limit. Subsequently, the analysis is expanded to an irreversible cycle and the relevant relationships are obtained for net work, thermal efficiency, total entropy production, and second law efficiency defined as the thermal efficiency of the irreversible cycle divided by the thermal efficiency of the ideal cycle. The effects of the compressor and turbine efficiencies, regenerator effectiveness, pressure drop in the cycle and the ratio of maximum-to-minimum cycle temperature on optimum pressure ratios obtained by maximization of 1st and 2nd law efficiencies and work output are examined. The results indicate that for the regenerator effectiveness greater than 0.82, the 2nd law efficiency optimization may be considered as a trade-off between the maximum work output and the maximum 1st law efficiency. (C) 2013 Elsevier Ltd. All rights reserved.