Heat from compression processes is normally wasted to cooling water due to its low temperature or concerns about operability. The recoverable amount of heat can be enhanced by increasing the operating temperature of compressors. However, the compression work also increases under this condition. The integration of compressors into heat exchanger networks (HENs) is complex since both heat and work are involved, and the role of streams (as hot or cold streams), the utility demand, and the location of pinch points may change. A systematic graphical design procedure for above ambient HEN design including compressors was presented. The objective is to minimize exergy consumption to balance the complex heat-work trade-offs involved. Four theorems are proposed as the basis of the design procedure with certain well-defined assumptions. It is found that the compression should be performed at pinch or ambient temperatures to achieve minimum exergy consumption. (c) 2015 American Institute of Chemical Engineers AIChE J, 61: 3770-3785, 2015