We study attribute-based regulations, under which regulatory compliance of a firm, product, or individual depends on a secondary attribute that is not the intended target of the regulation. We develop a theoretical model of the welfare consequences of attribute basing, including its distortionary costs and potential benefits. We then quantify these welfare consequences using quasi-experimental evidence from weight-based fuel economy regulations. We use bunching analysis to show that vehicle weight increased in response to regulation. We also leverage a policy change and develop a new method for analyzing double-notched policies to compare the costs and benefits of a specific attribute-based policy.