Multiple compressors in series with intermediate heat exchangers are frequently used to reduce compressor energy consumption or to limit compressor discharge temperatures when the overall compression ratio (initial suction pressure divided by the required final pressure) is large. The optimum number of stages can be fixed by economics (trade-off between capital investment and energy cost) or by equipment and/or process compressor discharge temperature limitations. The chemical engineering design literature contains several conflicting heuristics for designing multistage gas compression systems, and little information about the rationale behind these heuristics is provided. This paper explores several aspects of multistage compression systems including economics, equipment temperature limitations, and process temperature limitations. New heuristics are presented that give either the economic optimum or the temperature-limited number of stages as a function of the overall compression ratio.