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Given the bleak prospects for a global agreement on coordinated policies to mitigate climate change, political pressure is increasing among industrialized countries for unilateral abatement. A major challenge thereby is the appropriate response to the threat of emissions leakage. Border carbon adjustments and output-based allocation of emissions allowances can increase effectiveness of unilateral action but introduce distortions of their own. We assess the relative attractiveness of these anti-leakage measures as a function of the abatement coalition size. We first develop a partial equilibrium analytical framework to gain generic insights on how these instruments affect emissions within and outside the coalition. We then employ a large-scale computable general equilibrium model of international trade and energy use to assess the cost-effectiveness of alternative anti-leakage strategies as the coalition evolves toward global coverage. We find that full border adjustments rank first in global cost-effectiveness, followed by import tariffs and then output-based rebates. The differences across anti-leakage measures and the overall appeal of such measures decline with the size of the abatement coalition. In terms of cost incidence, the abatement coalition prefers border carbon adjustments over output-based rebates; the opposite holds true for countries outside the coalition.