The sample size required for a given type I and type II errors of linkage decision is determined by using the earlier proposed method of the linkage test power estimation [Ginsburg et al., 1996]. Dependence of the sample size on the heterozygotic genotype penetrance is investigated. Two approaches to sample size reduction are considered: the choice of marker gene and the special extension of analyzed pedigree structures. Their effects are quantitatively evaluated in some illustrative situations. It is shown that a practical reduction in sample size can be achieved only when the added part of a pedigree has a special set of phenotypic characteristics in its members.