A three-stage pulse-tube cryocooler, in which the third stage pulse tube is arranged below the second stage pulse tube, with a gas flow conduit between the second stage pulse tube heat exchanger and the cold end of the second stage regenerator. The design of the invention is much simpler than a conventional three-stage parallel pulse tube cooler, requiring only two pulse tubes at the warm (room temperature) end and two reservoirs, with a corresponding reduction in the number of associated orifices, passages, etc. In effect, this provides a three stage cryocooler with a two-stage warm end design by putting the second and third stage pulse tubes in series, with a gas flow passage providing gas flow between the second and third stages for gas expansion and refrigeration. The three-stage design allows an intermediate temperature connection between the temperatures of the first and third stages, for applications which require three cooling temperatures.