Three desirable properties for any method of selecting a subset of evolutionary units (EUs) for conservation or for genomic sequencing are discussed. These properties are spread, stability, and applicability. We are motivated by a practical case in which the maximization of phylogenetic diversity (PD), which has been suggested as a suitable method, appears to lead to counterintuitive collections of EUs and does not meet these three criteria. We define a simple greedy algorithm (GreedyMMD) as a close approximation to choosing the subset that maximizes the minimum pairwise distance (MMD) between EUs. GreedyMMD satisfies our three criteria and may be a useful alternative to PD in real-world situations. In particular, we show that this method of selection is suitable under a model of biodiversity in which features arise and/or disappear during evolution. We also show that if distances between EUs satisfy the ultrametric condition, then GreedyMMD delivers an optimal subset of EUs that maximizes both the minimum pairwise distance and the PD. Finally, because GreedyMMD works with distances and does not require a tree, it is readily applicable to many data sets.