While the employment effects of minimum wages are usually reported to be small (suggesting low substitutability between skill types), direct estimates suggest a much larger degree of substitutability. This paper argues that this paradox is largely due to a bias induced by the aggregation of skill types into broad categories. An assignment model is applied where skilled workers have a comparative advantage in complex jobs. The implied pattern of substitutability reveals the sources of the bias. Estimation results for the United States show elasticities of complementarity to be underestimated by up to a factor 2.5. The methods laid out can likewise be applied to other markets where different quality types are close substitutes, like the housing market.