A variant of Rayleigh-Schrödinger peturbation theory is applied to the computation of the additional power losses and phase shifts caused by perturbations of optical resonators. Numerical results are given for tilted infinite-strip plane resonators. For a large range of Fresnel numbers and sufficiently small angles of tilt, there is good agreement between these and previous results. The major advantages of this technique are its applicability for both high Fresnel numbers and higher-order modes with only a minimal use of computer time.