Frequently the problem of fitting distributions of the form (1) is ill posed, meaning that many different solutions will fit the data statistically indistinguishably well (Louis 1989; Hansen 1998; Engl et al. 2000) . For example, Provencher (1982) has illustrated this point via the Lemma of Riemann-Lebesgue, showing that one should expect a large set of very different solutions to fit the data equally well within the experimental error. In practice, noise of the data can amplify to determine even the overall features of the best-fit solution c; and often the strictly best-fit solution consists of a series of spikes whose number, location, and height may not reflect the presence of such species in the physical experiment, but are governed by the details of the noise and other imperfections in the data.