Several projects investigating genetic function and evolution through sequencing and comparison of multiple genomes are now underway. These projects consume many resources, and appropriate planning should be devoted to choosing which species to sequence, potentially involving cooperation among different sequencing centres. A widely discussed criterion for species choice is the maximisation of evolutionary divergence. Our mathematical formalization of this problem surprisingly shows that the best long-term cooperative strategy coincides with the seemingly short-term "greedy" strategy of always choosing the next best single species. Other criteria influencing species choice, such as medical relevance or sequencing costs, can also be accommodated in our approach, suggesting our results' broad relevance in scientific policy decisions.