The objective in the construction of models of software quality is to use measures that may be obtained relatively early in the software development life cycle to provide reasonable initial estimates of the quality of an evolving software system. Measures of software quality and software complexity to be used in this modeling process exhibit systematic departures of the normality assumptions of regression modeling. Two new estimation procedures are introduced, and their performances in the modeling of software quality from software complexity in terms of the predictive quality and the quality of fit are compared with those of the more traditional least squares and least absolute value estimation techniques. The two new estimation techniques did produce regression models with better quality of fit and predictive quality when applied to data obtained from two software development projects.>