One central question of climate justice is how to fairly allocate the global emissions budget. Some commentators hold that the concept of fairness is hopelessly equivocal on this point. Others claim that we need a complete theory of distributive justice to answer the question. This paper argues to the contrary that, given only weak assumptions about fairness, we can show that fairness requires an allocation that is at least as prioritarian as the equal per capita view. Since even the equal per capita view is more prioritarian than is politically feasible, fairness is univocal enough for all practical purposes.