Nonlinear income taxes and linear commodity taxes are analyzed when people differ with respect to ability, high-skill agents have heterogeneous preferences, and neither individual abilities nor preferences are observable. We characterize pure income tax optima, which may be bunching or separating optima. In particular, the income tax may not be able to distinguish between those low-income people who are low-skill and those who have a strong preference for leisure. As is shown, there may still be an effect on the optimum income tax schedule, as it will depend on the composition of the population with respect to types of individuals. Finally, the paper addresses what can be achieved by commodity taxes when preferences are heterogeneous - in particular, with respect to targeting groups that the income tax is incapable of discriminating between.