Although addressing climate change will ultimately require global cooperation, substantial progress may be achieved through small clubs of countries, where it is easier to forge and implement deals needed for policy coordination. Here we quantify the gains from cooperation in the arctic region and find that nearly 90% of the potential for abating black carbon can be reached by countries acting in self-interest alone because soot, the main source of black carbon, causes severe harm to human health along with warming. Abating methane, by contrast, requires more cooperation because impacts are more diffused geographically. Well-designed clubs with as few as four members can realize more than 80% of the full group cooperation potential for reducing these pollutants. The pivotal player in every effective club is Russia - most other members of the Arctic Council, the institution most focused on advancing the collective interests of the region, offer little leverage on the problems at hand.