In the basic model of international environmental agreements (IEAs) (Barrett 1994, Rubio and Ulph 2006) extended by international trade, self-enforcing - or stable - IEAs may comprise up to 60 % of all countries (Eichner and Pethig 2013). But these IEAs reduce total emissions only slightly compared to non-cooperation. Here we analyze the capacity of sign-unconstrained tariffs to enhance the size and performance of self-enforcing IEAs. We show that the size of stable IEAs shrinks when climate coalitions are Stackelberg leaders and set tariffs in addition to their cap-and-trade schemes. Surprisingly, these smaller IEAs reduce total emissions more effectively than the larger stable IEAs without tariffs. In the model with tariffs the signatory countries import fossil fuel and their tariff takes the form of a subsidy of fuel consumption and a tax on the production of the consumption good.