The analytic eigenfunction inversion technique to retrieve aerosol columnar size distributions from Mie extinction measurements has been extended to include a priori information, specifically surface area. The earlier (standard) and new (subtracted) techniques are compared by use of synthetic data that cover typical aerosol size distributions. Two different measurement wavelength ranges are considered. It is shown that the most appropriate inversion technique depends on the particle sizes, with the standard technique being more appropriate for small particles and the subtracted being more appropriate for large particles. Also presented is a simple method to determine whether a particular inversion technique is likely to produce meaningful results with a particular data set.