The coefficient of performance (COP) of pulse tube coolers is mainly determined by irreversible processes in the regenerator. In this paper, a general and basic definition for the efficiency of regenerators is proposed. The efficiency of the regenerator, and consequently of the cooler as a whole, is affected by the system which is used to control the pressure in the tube. For a general pressure-wave form, it is shown that in the optimum situation, under certain conditions, the variation of the pressure in the tube is proportional to the variation of the pressure in the compressor. In that case the COP is independent of the form of the pressure wave.