We develop a framework to study “attribute-based regulations,” under which regulatory compliance of a firm, product, or individual depends upon a secondary attribute that is not the intended target of the regulation. Many important economic policies are attribute-based, but economists have given the phenomenon little attention. Our model characterizes the welfare consequences of attribute basing, including its distortionary costs and potential benefits. We empirically test the model predictions by exploiting quasi-experiments in Japanese fuel-economy regulations, under which fuel-economy targets are declining step functions of vehicle weight. Using bunching analysis, we identify that the attribute-based fuel-economy regulation induced significant distortionary in- creases in vehicle weight. Our model also shows conditions under which attribute basing provides efficiency or distributional benefits, at the cost of distorting the attribute. We empirically quantify this welfare trade-off by developing counterfactual simulations based on incentives created by “double-notched” policies.