Heat can be converted into work and vice versa, and this fact provides opportunities for the integration between them. This paper presents a systematic methodology for the integration of compressors into heat exchanger networks below ambient temperature. The objective is to minimize exergy consumption. Four theorems are proposed and used as the basis for the design methodology. Pinch Compression, i.e., compression starts at pinch temperature, is proven to be preferred under certain conditions. It is concluded that minimum exergy consumption can be achieved when compression starts at pinch temperatures, ambient temperature or the cold utility temperature. (C) 2015 Elsevier Ltd. All rights reserved.