Among college graduates, teachers have both low average AFQT and high average risk aversion, perhaps because the compression of earnings within teaching attracts relatively risk-averse individuals. Using a dynamic optimization model with unobserved heterogeneity, we show that were it possible to make teacher compensation mimic the return to skills and riskiness of the non-teaching sector, overall compensation in teaching would increase. Moreover, this would make many current teachers substantially worse off, making reform challenging. Importantly, our conclusions are sensitive to the degree of heterogeneity for which we allow. Since even a model with no unobserved heterogeneity fits well within sample, one could easily conclude that allowing for two or three types fits the data adequately. Formal methods reject this conclusion. The BIC favors seven types. Ranking models using cross-validation, nine types is better although the improvements of going from six to seven, from seven to eight and from eight to nine types are noticeably smaller than those from adding an additional type to a lower base.