The problem of inverting aerosol extinction data in the near-UV to near-IR range to retrieve aerosol size distributions is addressed by means of a recently developed method called "synthesis inverse mapping." The rationale and the algebra of the method are developed, and the full error budget is discussed. The performance of the algorithm is evaluated with respect to standard monomodal and bimodal distributions published in the literature. The new method allows error amplification control and estimation of the smoothing error, and it is well suited for operational fast retrieval.