The analyses of the primary objectives of randomized clinical trials often are not adjusted for covariates, except possibly for stratification variables. For analyses with linear models, adjustment is a precision issue only. We review the literature regarding logistic and Cox (proportional hazards) regression models. For these nonlinear analyses, omitting covariates from the analysis of randomized trials leads to a loss of efficiency as well as a change in the treatment effect being estimated. We recommend that the primary analyses adjust for important prognostic covariates in order to come as close as possible to the clinically most relevant subject-specific measure of treatment effect. Additional benefits would be an increase in efficiency of tests for no treatment effect and improved external validity. The latter is particularly relevant to meta-analyses.