One can obtain population-based estimates of the penetrance of a measurable mutation from cohort studies, from population-based case-control studies, and from genotyped-proband designs (GPD). In a GPD, we assume that representative individuals (probands) agree to be genotyped, and one then obtains information on the phenotypes of first-degree relatives. We also consider an extension of the GPD in which a relative is genotyped (GPDR design). In this paper, we give methods and tables for determining sample sizes needed to achieve desired precision for penetrance estimates from such studies. We emphasize dichotomous phenotypes, but methods for survival data are also given. In an example based on the BRCA1 gene and parameters given by Claus et al. [(1991) Am J Hum Genet 48:232-242], we find that similar large numbers of families need to be studied using the cohort, case-control, and GPD designs if the allele frequency is known, though the GPDR design requires fewer families, and, if one can study mainly probands with disease, the GPD design also requires fewer families. If the allele frequency is not known, somewhat larger sample sizes are required. Surprisingly, studies with mixtures of families of affected and non-affected probands can sometimes be more efficient than studies based exclusively on affected probands when the allele frequency is unknown. We discuss the feasibility and validity of these designs and point out that GPD and GPDR designs are more susceptible to a bias that results when the tendency for an individual to volunteer to be a proband or to be a subject in a cohort or case-control study depends on the phenotypes of his or her relatives.