The authors study the properties of imbalances tests of predetermined characteristics (covariates) in stratified randomized controlled trials. When the parameter of interest is a weighted average of the causal effects at all strata, then a test statistic based on a fixed effects regression model may suffice to detect the relevant imbalances. This will be true under a condition on the partial correlation between covariates and the outcome variable (uniformity condition). If that condition is violated, then the test based on the fixed effects regression will lack power. In that case, a test based on the fully saturated regression model can overcome this problem. Finally, the authors provide an omnibus test for the relevance of controlling for the covariates when estimating the average treatment effect (ATE).