An unbiased estimate of the rate ratio can be obtained using a case-control design in which each case is matched to one or more controls randomly selected from population members at risk and in the same stratum as the case at the time of disease onset. However, the nonrandom assignment of controls to cases is quite frequent in case-control research. It occurs, for example, in matched case-control studies using either friend controls or neighborhood controls. Many valid random designs, in contrast to most nonrandom designs, require enumeration of a substantial fraction of the study base. Therefore, there may be important cost and logistic advantages to using valid nonrandom designs. In this paper we determine those nonrandom case-control designs that can produce unbiased estimates of the rate ratio and discuss the implications of our findings for the design of case-control studies. We conclude, as did Flanders and Austin, that friend-case-control studies should generally be avoided. On the other hand, in a typical neighborhood-matched, case-control study, any bias attributable to nonrandom control selection is usually too small to affect substantive conclusions.