Structural change reduces aggregate productivity growth by reallocating production to industries that have low productivity growth. We document that this so-called Baumol disease considerably reduced productivity growth in the postwar U.S. We build a model of structural change that captures the effect of Baumol disease on productivity growth. Our model allows for the often overlooked reallocation of production between services with fast and slow productivity growth. Connecting the model to the data implies that the two are substitutes. We show that this limits the importance of services with slow productivity growth and the future effect of Baumol disease.