A method of extending moments method calculations for monoenergetic, point isotropic gamma ray sources to depths of approximately 50 mean-free-paths is described. Sample calculations are given for water and aluminum. A method of error analysis recently developed by Spencer suggests that for the range from 10 to ∼50 mean-free-paths, the errors associated with the reconstruction of the flux from moments are generally <1%. Comparisons are made between the asymptotic, deep penetration trend of the calculated results and the trend predicted by a theory developed by Fano.