Protecting biodiversity involves preserving the maximum number and abundance of species while giving special attention to species with unique genetic or morphological characteristics. In balancing different priorities, conservation policymakers may consider quantitative measures that compare diversity across ecological communities. To serve this purpose, a measure should increase or decrease with changes in community composition in a way that reflects what is valued, including species richness, evenness, and distinctness. However, counterintuitively, studies have shown that established indices, including those that emphasize average interspecies phylogenetic distance, may increase with the elimination of species. We introduce a new diversity index, the phylogenetic entropy, which generalizes in a natural way the Shannon index to incorporate species relatedness. Phylogenetic entropy favors communities in which highly distinct species are more abundant, but it does not advocate decreasing any species proportion below a community structure-dependent threshold. We contrast the behavior of multiple indices on a community of phyllostomid bats in the Selva Lacandona. The optimal genus distribution for phylogenetic entropy populates all genera in a linear relationship to their total phylogenetic distance to other genera. Two other indices favor eliminating 12 out of the 23 genera.