Output-based carbon regulations—such as fuel economy standards and the rate- based standards in the Clean Power Plan—create well-known incentives to inefficiently increase output. Similar distortions are created by attribute-based regulations. This paper demonstrates that, despite these distortions, output and attribute-based standards can always yield greater expected welfare than “flat” emission standards given uncertainty in demand for output (or attributes), assuming locally constant marginal damages. For fuel economy standards, the welfare-maximizing amount of attribute or mileage-basing is likely small relative to current policy. For the electricity sector, however, an intensity standard may yield greater expected welfare than a flat standard.