I develop a general equilibrium model featuring multidimensional skills and partial specialization in tasks to quantify the impact of several determinants on within-occupation inequality growth from 1980 to 2000. The model introduces a new mechanism by which demand shifts affect inequality: Workers within the same occupation perform multiple and different tasks. I structurally estimate the model using microdata and account for inequality growth due to three sources: changes in occupation demand, changes in the task content of occupations, and changes in labor composition. My findings indicate that changes in task content explain the majority of within-occupation inequality growth. (JEL D63, J21, J22, J23, J24)