Objective Randomized controlled trials (RCTs) with dichotomous outcomes may be analyzed with or without adjustment for baseline characteristics (covariates). We studied type I error, power, and potential reduction in sample size with several covariate adjustment strategies. Study Design and Setting Logistic regression analysis was applied to simulated data sets (n=360) with different treatment effects, covariate effects, outcome incidences, and covariate prevalences. Treatment effects were estimated with or without adjustment for a single dichotomous covariate. Strategies included always adjusting for the covariate ("prespecified"), or only when the covariate was predictive or imbalanced. Results We found that the type I error was generally at the nominal level. The power was highest with prespecified adjustment. The potential reduction in sample size was higher with stronger covariate effects (from 3 to 46%, at 50% outcome incidence and covariate prevalence) and independent of the treatment effect. At lower outcome incidences and/or covariate prevalences, the reduction was lower. Conclusion We conclude that adjustment for a predictive baseline characteristic may lead to a potentially important increase in power of analyses of treatment effect. Adjusted analysis should, hence, be considered more often for RCTs with dichotomous outcomes.