We investigate how different designs of carbon offset mechanisms, like the Kyoto Protocol's Clean Development Mechanism (CDM), affect the success of self-enforcing climate treaties. In a game-theoretic numerical model of coalition formation we find that participation in the agreement is negatively affected when strategic behavior and free-rider incentives matter. This does not change when selling targets restrict credit supply. Substantially higher participation emerges when the treaty restricts its signatories not to use the gains from credit trading to lower their emission caps. Despite the high sensitivity of participation to different CDM design, we find that global welfare levels achieved in various equilibria are remarkably similar.