International environmental agreements have had varying success in the past; the theoretical literature on international environmental agreements (IEAs) explains why freeriding is so common. This paper allows for two strategically different types of countries. Damage functions are concave for some countries (contrary to the standard convexity assumption). This leads to strategic substitutes and complements in emissions reduction within the same model. The interaction of both country types can lead to a stable agreement that is larger than in the standard case, and to more global abatement. Such a stable agreement constitutes an island of stability in addition to the small standard agreement.