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Intensity standards have gained substantial momentum as a regulatory instrument in US climate policy. Energy-intensive and trade-exposed industries are traditionally opposed to initiatives for domestic carbon pricing as they are particularly vulnerable to competitiveness losses and refer to counterproductive emission leakage in a unilateral climate policy context. This has led to policy proposals where intensity standards on energy and carbon might at least in part substitute for explicit carbon pricing via taxes or emission allowances. In this paper we study the economic efficiency properties of intensity standards as an instrument of unilateral climate policy. We first develop a theoretical partial equilibrium framework and show that standards can have an ambiguous effect on carbon leakage. We then use an applied computable general equilibrium model of the global economy to gain quantitative insights into the effects of intensity standards for the case of the US. Our numerical results show that intensity standards may rather increase than decrease carbon leakage. Moreover, standards can lead to considerable welfare losses compared to uniform emission taxing. The tradability of standards across industries is a mechanism that can reduce these negative effects.