In this paper, a comparison between the Entropy Generation Minimization method and the Power Maximization technique is presented. The assessment is performed by analyzing, as a typical example of direct conversion heat engines, the thermoelectric generator. The effects of heat-leak and finite-rate heat transfer on the performance of the generator, which is modeled as a Carnot-like engine with internal irreversibilities, are studied. Even though both methods lead to the same conclusions, the entropy generation minimization method, when applied for such an inherently irreversible device, is shown to be less straight forward than the power maximization technique requiring careful accounting of the different sources of irreversibility. Moreover, the entropy generation rate vs. efficiency behavior of the generator reveals that the efficiency at minimum entropy generation rate and the maximum efficiency are distinct. (C) 2000 Elsevier Science Ltd. All rights reserved.