A synthesis of classical and recent thinking on the issues involved in selecting controls for case-control studies is presented in this and two companion papers (S. Wacholder et al. Am J Epidemiol 1992;135:1029-50). In this paper, a theoretical framework for selecting controls in case-control studies is developed. Three principles of comparability are described: 1) study base, that all comparisons be made within the study base; 2) deconfounding, that comparisons of the effects of the levels of exposure on disease risk not be distorted by the effects of other factors; and 3) comparable accuracy, that any errors in measurement of exposure be nondifferential between cases and controls. These principles, if adhered to in a study, can reduce selection, confounding, and information bias, respectively. The principles, however, are constrained by an additional efficiency principle regarding resources and time. Most problems and controversies in control selection reflect trade-offs among these four principles.