The EU steps up its efforts to curb its territorial CO2-emissions. It is planning to introduce a carbon border adjustment mechanism (CBAM) to level the playing field and to raise own resources. The authors point out that unilateral European climate policy action, whether shored up with a CBAM or not, can only play a limited role in reducing global CO2-emissions. A EU-CBAM cannot stop indirect leakage, it has ambiguous effects on other countries’ mitigation efforts, and it poses the risk of conflicts with trade partners. They propose that the EU, together with the US and other like-minded countries, should push hard to establish a climate club with a common minimum price of CO2 and a common CBAM applied to third countries. Such a framework would incentivize other countries to join while limiting leakage and reducing the risk of trade policy disputes.