 The effective population size is a crucial concept in population genetics, which measures the rate at which genetic drift affects a population. Diocese populations exhibit excesses of heterozygosity compared to menaceous panmictic populations as measured by Wright's FIS. This excess is negatively correlated with population size, and FIS can be used to estimate the eigenvalue effective population size of diocese populations. A new approximation has been proposed that provides a highly accurate estimate of the eigenvalue effective population size of a diocese population as a function of the real population size. The accuracy of different FIS-based methods using the leading eigenvalue of transition matrices or coalescence is explored, and it appears that the eigenvalue-based method provides more accurate results in very small populations. The applicability of this method in the field is also discussed. This article was authored by Demias, Thierry, and Nus, Camille.