This paper explores alternatives to the usual thermodynamic optimization formulation, where the thermodynamic performance of a system is improved subject to physical size constraints (e.g., entropy generation minimization). The alternative is to minimize the physical size subject to specified thermodynamic performance. It is shown that the alternate optimization leads to the same physical design-the same configuration-as the usual optimization. This is demonstrated by means of three examples: power plant model with two heat exchangers, power plant model driven by a hot stream of single-phase fluid, and refrigerator model with irreversibility due to imperfect insulation.