Three regression approaches are examined for use in estimating water solubilities and octanol/water partition coefficients, two fundamental equilibrium constants that are widely used in predicting the fate of organic chemicals in aquatic systems. Approaches examined are regression of solubility against partition coefficient, determination of the product of solubility and partition coefficient, and application from Yalkowsky and Valvani (J. Pharm. Sci., 69 (1980) 912). The regressions are based on data for water solubility, octanol/water partition coefficient, entropy of fusion, and melting point of 20 disperse and solvent dyes. In the study, all three methods produced more reliable data on dyes than other equations available in the literature. Root-mean-square deviations are on the order of a factor of four to six for all three methods. Factors such as purity, polymorphism, tautomerization, polarization and hydrogen bonding are suggested as factors precluding the development of highly reliable prediction relationships between solubility and partition coefficient of dyes. Sources of error in both the data and methodologies are discussed. The study also provided information on entropies of fusion, which ranged from 50.7 to 136 and averaged 78.8 J/mol K. Anthraquinone dyes exhibited much lower entropies of fusion than did azo dyes. Thus, use of an average entropy in estimation is inappropriate for dyes and leads to more error than neglecting the change in heat capacity. (Copyright (c) 1991 US Government.)