This paper examines the properties of the optimal nonlinear income tax when preferences are quasi–linear in leisure and individuals differ in their ability and their preferences for leisure. The government seeks to redistribute income. It can perfectly observe the level of endogenous income but cannot observe either ability or preferences. The heterogeneity of preferences leads to problems of comparability between individual utilities which challenge the design of redistributive schemes. We analyze the consequences of adopting a utilitarian social welfare function where the government is allowed to give different weights to individuals with different preferences. Under this particular social objective and given the quasi–linearity of preferences, we are able to obtain closed–form solutions for the marginal tax rates and to examine the progressivity of the tax system according to the weights used.