A number of small-sample corrections have been proposed for the conditional maximum-likelihood estimator of the odds ratio for matched pairs with a dichotomous exposure. I here contrast the rationale and performance of several corrections, specifically those that generalize easily to multiple conditional logistic regression. These corrections or Bayesian analyses with informative priors may serve as diagnostics for small-sample problems. Points are illustrated with a small exact performance comparison and with anexample from a study of electrical wiring and childhood leukemia. The former comparison suggests that small-sample bias may be more prevalent than commonly realized.Keywords: Bias; Case-control studies; Conditional logistic regression; Cox model; Epidemiologic methods; Likelihood analysis; Logistic models; Matching; Odds ratio; Proportional hazards; Relative risk; Risk assessment.