Countries engaged in climate change mitigation combine different instruments ranging from environmental regulations to cap-and-trade systems. In the absence of international coordination, by reducing their emissions, these countries however displace some production of emitting industries (direct effect) and depress the price of fossil fuels leading indirectly to higher emissions by non-constrained countries. The direct effect can be addressed by free allowances of emission quotas to energy intensive industries, or tentatively through a carbon adjustment at the border. However, none of these strategies relaxes the problem of indirect leakages, while the legal consistency of Carbon Border Adjustments (CBA) with the WTO law is questionable. This paper investigates different policies aiming at efficiently curb global emissions in a context where not all countries adopt a cooperative behavior. Taking stock of the unconditional Nationally Determined Contributions of countries member of the Paris Agreement, we compare different modalities of a CBA at the border of the EU 27 with alternative approaches like the Nordhaus-type Club. We conclude that CBA is difficult to implement and hardly reduces the leakages induced by the Paris agreement, as opposed to an ambitious climate Club. Although optimal from the social planner perspective such Club would hardly attract large countries by applying moderate tariffs at its borders.