In this paper, we describe an exact method for estimating a common relative risk across different epidemiologic study designs. The types of studies allowed by the method include case-control studies, follow-up studies with an internal comparison group, and follow-up studies with an external comparison group. Because the method is exact, sparseness of individual studies is not an issue. Those wishing to perform a meta-analysis of case-control studies and follow-up studies in which both the exposure and outcome are rare will find the method particularly useful. To allow one to perform the computations efficiently, we present a partial polynomial multiplication algorithm. We also describe a public-domain computer program that performs the necessary calculations.