This paper describes the optimization of the distribution of heat transfer (cooling) during the process of gas compression. The coolant is a stream of cold liquid. There is a fundamental tradeoff between the savings in compressor power, which are due to distributed cooling, and the pumping power required to circulate the coolant. The tradeoff is revealed on the basis of a combined model of multi-stage gas compression, resistance to fluid flow, and area-constrained counter- or co-current heat exchange between the gaseous stream and the liquid stream. The results are illustrated for the compressor of an actual ammonia refrigeration plant, for which the distributed-cooling design is highly recommended because the compressor discharge temperature in such units is high. It is shown that there is an optimal coolant (water) flow rate such that the total power requirement is minimized. The optimized distribution of gas compression and cooling is robust with respect to the selection of the water flow rate. (C) 2005 Elsevier Ltd. All rights reserved.