Non-cooperative game theoretical models of self-enforcing international environmental agreements (IEAs) that employ the cartel stability concept of D'Aspremont et al. (Can J Econ 16:17-25, 1983) frequently assume that countries are identical, and they can sign a single agreement only. We modify the assumption by considering two self-enforcing IEAs and also two types of asymmetric countries. Extending a model of Barrett (Oxford Econ Pap 46:878-894, 1994), we demonstrate that there are similarities between one and two self-enforcing IEAs. But in the case of few countries and high environmental damage we show that two self-enforcing IEA work far better than one self-enforcing IEA in terms of both welfare and environmental quality. Our simulation shows that only if all countries that have fewer benefits and higher cost from pollution abatement must build one coalition, there is hope that two myopic stable coalition can be formed. Moreover, if the cost-benefit functions of pollution abatement impose that the first myopic coalition is formed by countries, which have higher benefits and lower cost from pollution abatement, then two IEA's worsen abatement and welfare in comparison to one IEA. But, if the first myopic coalition is formed by countries, which have smaller benefits and higher cost from pollution abatement, then two IEA's improve abatement and welfare in comparison to one IEA. © 2010 Springer Science+Business Media, LLC.