The key component of a Stirling engine is its regenerative heat exchanger. This device is subject to losses due to dissipation arising from the flow through the regenerator as well as due to imperfect heat transfer between the regenerator material and the gas. The magnitudes of these losses are characterized by the Stanton number St and the Fanning friction factor f, respectively. Using available data for the ratio St/f, results are found for the Carnot efficiency and the power output of the regenerator. They depend on the conductance and on the ratio of pressures at the two sides of the regenerator. Optimum results for efficiency and power output of the regenerator are derived in the limit of zero Mach number. The results are applied to the Stirling engine. The efficiency and the power output of the engine are found for given amplitude of the compression piston. Optimization with respect to regenerator conductance and piston phase angle leads to a maximum possible value of the power output. Under optimal conditions, the Carnot efficiency just below this maximum is close to 100%. Copyright (C) 2009 John Wiley & Sons, Ltd.