This article presents a targeting and design methodology that can be implemented for any process where pressure-based exergy, also known as mechanical exergy, has an important contribution to the total exergy conversion and transfer. However, in this article it is applied to processes that operate at sub-ambient conditions, or processes where the ambient conditions are crossed. Exergy efficiencies, new Exergetic Composite Curves, Cascades, and Extended Grid Diagrams are tools that had to be implemented, improved, or invented, to develop a methodology with considerable potential for energy-efficient process design. The appropriate placement (correct integration) of compressors and expanders in heat exchanger networks is also analyzed to minimize the number of units. An example is used to demonstrate the methodology, where several simplifying assumptions are made to facilitate understanding and to explain the design method. (c) 2016 American Institute of Chemical Engineers