Abstract: Many people believe that the problem of climate change would be best handled by an international agreement that includes a system of cap and trade. Such a system would impose a global cap on greenhouse gases emissions and allocate tradable emissions permits. This proposal raises a crucial but insufficiently explored question: How should such permits be allocated? It is tempting to suggest that in principle, allocation should be done on a per capita basis, with the idea that each person should begin with the same entitlement, regardless of place of birth. This idea, pressed by many analysts and by the developing world, can be defended on grounds of either welfare or fairness. But on both grounds, per capita allocations run into serious objections. If fairness is understood in terms of equally or proportionally sharing the burdens of a climate treaty, per capita allocations are not fair because they do not take into account all the effects of such a treaty. Any agreement to reduce greenhouse gas emissions will give more benefits to some nations than to others, and will impose more costs on some nations than on others; in these circumstances, per capita emissions rights give the appearance but not the reality of fairness. For those who seek redistribution to those who need help, on grounds of either welfare or fairness, per capita allocations of emissions rights are at best a mixed blessing. Some rich nations are highly populated, and some poor nations have small populations; there is essentially no relationship between size of population and per capita wealth. Per capita allocations would also create serious incentive problems, and they would face decisive objections from the standpoint of feasibility: Per capita rights would transfer hundreds of billions of dollars annually from the United States to China and India, and the United States is most unlikely to sign a treaty with that consequence. Comparisons are drawn between per capita allocations and other approaches, including those based on existing emissions rates and those with self-conscious redistributive aims. A general goal is to balance welfarist and fairness goals with feasibility constraints; per capita allocations do a poor job of achieving that balance, and an insistence on that approach might make the climate change problem intractable. These conclusions have general implications for thinking about normative goals and practical limitations in the context of international law.