Abstract: Regarding thermomechanical engines, the first law efficiency has been until now, the most used criterion, with the famous equilibrium thermodynamics upperbound given by the CARNOT formula. Most recently (second part of the past century), a new appraisal appears, regarding the maximum power objective for the engines. We propose here to reconsider these two main approaches due to the fact that the heat expanses first, and the heat rejected secondly are also involved in the complete characterization of the engine. These three quantities (energy consumption to minimize associated to the cost ; useful effect to maximize ; heat rejection to minimize, in order to protect the environment) are combined through a weighting procedure allowing, to discuss and choose the best scheme. Particular previous studies results are recovered and synthesized. Other new possibilities are proposed to be explored in the near future.