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In a recent review an optimal thermodynamics and associated new upper bounds have been proposed, but it was only relative to power delivered by engines. In fact, it appears that for systems and processes with more than one utility (mainly mechanical or electrical power), energy conservation (First Law) is limited for representing their efficiency. Consequently, exergy analysis combining the First and Second Law seems essential for optimization of systems or processes situated in their environment. For thermomechanical systems recent papers report on comparisons between energy and exergy analysis and corresponding optimization, but the proposed models mainly use heat transfer conductance modelling, except for internal combustion engine. Here we propose to reconsider direct and inverse configurations of Carnot machines, with two examples. The first example is concerned with “thermofrigo-pump” where the two utilities are hot and cold thermal exergies due to the difference in the temperature level compared to the ambient one. The second one is relative to a “combined heat and power” (CHP) system. In the two cases, the model is developed based on the Carnot approach, and use of the efficiency-NTU method to characterize the heat exchangers. Obtained results are original thermodynamics optima, that represent exergy upper bounds for these two cases. Extension of the proposed method to other systems and processes is examined, with added technical constraints or not. Full article