Non-linear income taxes and linear commodity taxes are analysed when people differ with respect to ability, high-skilled agents have heterogeneous preferences, and neither individual abilities nor preferences are observable. The paper highlights how informational constraints may motivate differential treatment of people with different preferences for leisure even if unequal treatment is not desirable per se. Which preference type will be better or worse off is shown to depend on the self-selection constraints associated with the information asymmetry. 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 lowincome people who are low-skilled and those who have strong preference for leisure. As is shown, there may still be an impact 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, in terms of targeting groups that the income tax is incapable of discriminating between.