The comparisons of treatments in randomized clinical trials may use the analysis of covariance to adjust for patient characteristics. We present theoretical results that describe when such an adjustment would be expected to be beneficial. A distinction is made between covariates that are balanced in the design and those that are assigned by the randomization process. The results support the commonly held view that features balanced in the design of the trial (e.g., by stratification) and those that are strongly predictive of the outcome, and thus considered clinically prognostic, should normally be included in the analysis. For other covariates that are not balanced in the design, the potential benefits of including them in the analysis will depend on the number of patients in the trial. However, there is frequently a set of variables whose relevance is unknown and for which data-dependent methods of selection, based on the data for the current trial, have been proposed. A review of the literature has shown that these methods can produce misleading inferences. The decision as to which covariates to include in the analysis should be specified in the protocol on the basis of data from previous trials on similar patient populations. The methods are illustrated with data from a trial comparing two therapies for treating scalp psoriasis where the clinical importance of patients' age and sex as prognostic factors for efficacy is unknown. We show for what size of future trials it would be beneficial to adjust for these covariates and for what size trials it would not. In all cases, prespecification of variables to be included in the analysis is essential in order to avoid bias.