This paper considers the basic thermodynamic optimization problem of extracting the most power from a stream of hot exhaust when the contact heat transfer area is fixed. It shows that when the receiving (cold) stream boils in the counterflow heat exchanger, the thermodynamic optimization consists of locating the optimal capacity rate of the cold stream. At the optimum, the cold side of the heat transfer surface divides itself into three sections: liquid preheating, boiling and vapor superheating. Numerical results are developed for a range of design parameters of applications with either water or toluene on the cold side. It is shown that the optimal design is robust, because several of the design parameters have only a weak effect on the optimal design.