For the United States, the supply and wages of skilled labor relative to those of unskilled labor have grown over the postwar period. The literature has tended to explain this through “skill-biased technical change” (SBTC). Empirical work has concentrated around two variants: (1) capital-skill complementarity, (2) skill-augmenting technical change. Our purpose is to nest and discriminate between these two explanations. We do so in the framework of multilevel Constant Elasticity of Substitution (CES) production function, where factors are disaggregated into skilled and unskilled labor, and capital into structures and equipment capital. Using a five-equation system approach and several nesting alternatives, we retrieve estimates of the substitution elasticities and technical changes. Our estimations can produce results in line with capital-skill-complementarity hypothesis. However, those results are outperformed where the only source of the widening skill premium has been skill-augmenting technical change. We also show that the different explanations for SBTC have different implications for projected developments of the premium.