The performance of Stirling engines is subject to limitations resulting from power dissipation in the regenerator. The dissipation is caused by pressure gradients in the regenerator required to generate flow. Without this flow the power output would be zero. Hence the dissipation is an essential element of the operation of the engine. Using linearized theory, the pressure in the compression and expansion spaces is found as a function of the ratio of piston amplitudes and piston phase difference. The regenerator is taken to be thermally perfect. All variations are taken to be sinusoidal in time. Expressions are derived for the dimensionless power output and the thermal efficiency at a given amplitude of the compression piston. Upper bounds on the power output and the efficiency are found as function of frequency and of regenerator void volume. Special attention is given to the case of piston amplitude ratio equal to 1.