This paper compares stability of international environmental agreements for six different rules of coalition formation under very general conditions (any type of heterogeneity between countries). The rules can be interpreted as different institutional settings in which treaty formations take place and/or different designs of agreements. We consider open and restricted open membership game as well as four exclusive membership games with different degrees of unanimity required to form coalitions. From a policy perspective, counterintuitively, it turns out that stability is higher under exclusive than under open membership and stability increases with the degree of unanimity. We discuss the policy implications of our result for future treaty-making.