Contrary to the impression given in some textbooks, matching can reduce the efficiency of a cohort study, even when it produces no sample-size reduction and even if the matching variable is a confounder. The authors illustrate this along with some additional points regarding cohort matching. First, the impact of matching on efficiency can be in opposite directions for different measures of effect; as a consequence, criteria for deciding whether to match must depend on whether one wishes to estimate relative or absolute effects. Second, the commonly drawn analogy between blocking in randomized trials and matching in cohort studies is misleading when one considers the impact of matching on covariate distributions. Third, the conditions for efficiency overmatching in a cohort study are different from the conditions in a case-control study. It appears that, under an additive model, matching will usually increase the efficiency of both risk-difference and risk-ratio estimation, and the power of the Mantel-Haenszel test. Under a multiplicative model, the impact of matching is not as consistently beneficial. The authors present some approximate criteria which allow one to use a priori information to predict whether cohort matching is likely to improve efficiency.