Bias and power are compared for the stratified and unstratified logrank tests in survival type studies with censored data. It is assumed that strata are formed by grouping a covariate. Bias arises when covariate values differ between groups. Survival may then be equal at each covariate value, but appear to differ overall. Large sample findings indicate that 3–4 strata suffice to accomplish most of the potential gain relative to the unstratified situation. Gains are worthwhile for bias, but small for power unless the response and covariate are strongly correlated. In small samples the increase in power with stratifica tion may be even less. Equal frequency and optimal strata usually give similar results.