The method of isonymy, developed by Crow and Mange for estimating inbreeding from surname frequencies, requires an assumption that has not been appreciated: It is necessary to assume that all males in some ancestral generation, the founding stock, had unique surnames. Because this assumption is seldom justified in real populations, the applicability of the isonymy method is extremely limited. Even worse, the estimates it provides refer to an unspecified founding stock, and this implies that these estimates are devoid of information.