A key challenge for unilateral policy initiatives, even for a big coalition like the EU, is carbon leakage and competitiveness concerns. A problem with international climate agreements is also that few countries will sign an abatement agreement due to the free rider problem: all countries benefit whereas cost of abatement is born entirely by the country itself. We analyze economic and emission effects of introducing carbon taxes combined with output-based rebating. We also analyze how a border tax improves the attractiveness of international climate agreements and increases the number of signatories. The design of subsidy policies for abatement technology will also influence the competitiveness of firms and carbon leakage, and the effects may differ between large versus small regions/countries. We use both theoretical and numerical methods, the last one exemplified by the global CGE model SNoW.