A method for determining Doppler broadening which is rigorous for a Maxwellian gas of resonance absorber atoms has been reduced to computation. Doppler broadened absorption cross sections for low-lying resonances of Er167 and Xe135 have been computed both by this more accurate method and by the ψ-function approximation which is in general use. The more accurate method was found to give a correction, compared with the ψ-function method, which was several percent in the case of Xe135 and was less than 1 % for Er167. The time required for the more accurate computation was found to be short enough to be practical for those special applications wehere it is of interest.