Business cycles may be defined or measured by parametrizing detrending filters to maximize the ability of a business-cycle model to match the moments of the remaining cycles. Thus a theory can be used to guide cycle measurement. We present two applications to U.S. postwar data. In the first application the cycles are measured with a standard, real business cycle model. In the second, they are measured using information on capacity utilization and unemployment rates. Simulation methods are used to describe the properties of the GMM estimators and to allow exact inference.