We examine the power of different exact tests of differentiation for diploid populations. Since there is not necessarily random mating within populations, the appropriate hypothesis to construct exact tests is that of independent sampling of genotypes. There are two categories of tests, FST-estimator tests and goodness of fit tests. In this latter category, we distinguish "allelic statistics", which account for the nature of alleles within genotypes, from "genotypic statistics" that do not. We show that the power of FST-estimator tests and of allelic goodness of fit tests are similar when sampling is balanced, and higher than the power of genotypic goodness of fit tests. When sampling is unbalanced, the most powerful tests are shown to belong to the allelic goodness of fit group.