Adjustment for prognostic covariates is recommended in clinical trials because relative to a t-test, it improves precision and adjusts for treatment imbalances caused by an "unlucky" randomization. But, inclusion of too many covariates can be counterproductive. In the quest to strike a balance between inclusion of all important variables and not going overboard, people have proposed methods such as stepwise regression, whereby the decision to include a covariate depends on post-randomization data. Covariate inclusion decisions are typically based on either the strength of its correlation with the outcome or the degree of treatment imbalance. Are these methods valid? Is there a valid way to analyze such data? These are some of the questions we address.