In developing an appropriate figure of merit for short wavelength, high power lasers, due consideration must be given to the application of the laser. For most high-power applications, energy or power delivered into a given solid angle in the far field is a suitable criterion. Performance measures appropriate to imaging systems are too stringent for energy delivery systems, and place too much emphasis on phase perturbations. Using the concepts of intensity-weighted average quantities, developed by Talanov, we derive a formalism to describe aberrated beams. Three types of aberrations are identified: Seidel, periodic, and stochastic. We find that stochastic aberrations mimic diffraction in their effect, and are more important than diffraction at short wavelengths. Materials limitations on short wave-length laser performance are discussed.