A model is developed to estimate the effect of covariate imbalance on the size of a test of treatment efficacy in randomized clinical trials comparing two treatments when dispersion parameters are known. It is concluded that tests of homogeneity on the covariates should not be performed, that covariate imbalance is just as much a problem for large studies as for small ones in terms of effect on size, and that the effect of correlation between covariates and measures of efficacy is more complex than has previously been suggested. The best way to adjust for covariate imbalance is by an analysis of covariance.