To take account of the observed lack of fit of the power law near thresh-old intensities, two different modifications of the power law have been proposed by various investigators. In this paper, both of these two laws are derived as a special case of a generalized power function for ratio scaling. A method is presented for discriminating between the special laws which provides (i) a prescription for the manipulation of independent variables, and (ii) specification of theoretical curves to which empirical curves are to be compared. Maximum-likelihood estimators are derived for the exponents of the special laws under the assumption that the observed subjective ratios are log normal.