Modeling breakage by a rate kernel that is power-law in particle size and with self-similar daughters yields similarity solutions of the population balance equations. For rate exponents that are inverses of integers, the moments of the similarity solution are easily found. Using a generalized power-law product daughter distribution that is self-similar and obeys the Hill-Ng exchangeability principle provides a very flexible description of the daughters. This paper explores how to interpret milling data to extract the parameters of the model, including the power-law exponent and either the sharpness parameter of the daughter distribution or the number of daughters in a breakup event. (c) 2005 Elsevier B.V All rights reserved.