Confounding is examined from first principles. In follow-up studies a confounder is a predictor of diagnosing the illness--by being either a risk indicator or a determinant of diagnostic errors; in addition, it shows different distributions between the exposed and nonexposed series. In case-referent studies confounding can arise in two ways. A priori confounders are correlates of exposure in the joint source population of cases and reference subjects; also, they are determinants of diagnosing the illness or have different selection implications between cases and referents. In addition, factors bearing on the accuracy of exposure information are confounders if distributed differently between cases and referents. Criteria based singularly on relationships in the data can be misleading. Similarly, a change in the estimate and even a change in the parameter as a result of control is not a criterion rooted in first principles of confounding and can lead to a false conclusion.