Carbon leakage provides an efficiency argument for differentiated emission prices in favor of emission-intensive and trade-exposed sectors under unilateral climate policy. However, differential emission pricing can be used as a beggar-thy-neighbor policy to exploit terms of trade. Adopting an optimal tax framework, we propose a method to decompose the leakage and terms-of-trade motives for emission price differentiation. We employ our method for the quantitative impact assessment of unilateral climate policy based on empirical data. We find that the leakage motive yields only small efficiency gains compared to uniform emission pricing. Likewise, the terms-of-trade motive has rather limited potential for strategic burden shifting. We conclude that in many cases the simple first-best rule of uniform emission pricing remains a practical guideline for unilateral climate policy design.