Data fitting procedures both with and without correction for non-ideality are applied to experimentally measured concentration distributions of zinc-free insulin obtained over a wide range of experimental conditions (pH 2, 7, and 10, ionic strengths 0.05 and 0.1, t = 25 degrees C and 37 degrees C) using four different model self-association patterns based on known physico-chemical properties of insulin in solution and patterns already in the literature. It is shown that three of these must be considered satisfactory descriptions of the insulin system of equilibria in aqueous solution as judged by critical curve-fitting criteria. The significant differences, as well as common features of these are assessed by comparing the distribution of monomeric and polymeric forms at three insulin concentrations of practical utility, "serum", "pharmacological", and "physicochemical". The value of analysing protein self-association with the aid of explicit equations formulated for a specific model, even when it cannot be demonstrated to be unique, is discussed with particular reference to osmotic pressure measurements made by others on insulins modified by recombinant DNA techniques aimed at making them essentially monomeric.