Virtually all parametric statistical procedures have been shown to be special cases of canonical correlation analysis, which is a useful research methodology particularly when augmented by the calculation of canonical structure, index, and invariance coefficients. A logic for conducting stepwise canonical correlation analysis based upon evaluation of canonical communality coefficients is presented. The coefficients indicate how much of a variable's variance is reproducible from the canonical solution. Variables with the smallest communality coefficients may be deleted in a stepwise procedure as a direct analoque to stepwise backward multiple regression analysis. A heuristic demonstration of the technique involving two criterion variables and five predictor variables in a 7 by 7 correlation matrix is presented. The application provides more insight into the dynamics of social science phenomena, lessens the probability of Type II errors, and provides estimates of the generalizability of results. (Author/CM)