Aerodynamic windows, which consist of one or more jets of high velocity gas, are frequently used to allow the extraction of laser beams from the laser cavity when the beam power density is sufficiently high to preclude the use of solid windows. Turbulent shear layers at the edges of the jets can produce random phase errors in the laser beam that can substantially reduce the maximum power density to which the beam can be focused. Improved semiempirical methods of predicting shear layer optical quality, applicable to both low and high Mach number shear layers, are presented and shown to give reasonably good agreement with one set of measurements on compressible shear layers. A number of recommendations for improving the optical quality of shear layers are presented. Some of these recommendations offer the potential for substantial improvements in optical quality.