Climate effects of unilateral carbon policies are undermined by carbon leakage. To counteract leakage and increase global cost-effectiveness carbon tariffs can be imposed on the emissions embodied in imports from non-regulating regions. We present a theoretical analysis on the economic incentives for emission abatement of producers subjected to carbon tariffs. We quantify the impacts of different carbon tariff designs by an empirically based multi-sector, multi-region CGE model of the global economy. We find that firm-targeted tariffs can deliver much stronger leakage reduction and higher efficiency gains than tariff designs operated at the industry level. In particular, because the exporters are able to reduce their carbon tariffs by adjusting emissions, their competitiveness and the overall welfare of their economies will be less randomly and less adversely affected than in previously studied carbon tariff regimes. This beneficial distributional impact could facilitate a higher degree of legitimacy and legality of carbon tariffs