We characterize the solution to the optimal nonlinear income taxation problem if individuals face a minimum hours constraint that gives rise to labor supply responses along the extensive margin. We provide conditions for optimal marginal tax rates to be positive everywhere and derive a formula for the optimal participation taxes. This formula shows the additional forces in comparison to the pure extensive labor supply model, can easily be generalized to other contexts of extensive and intensive labor supply responses, and provides a new condition under which an Earned Income Tax Credit (EITC) can be ruled out. In addition, we develop a test for the second-best Pareto-efficiency of any income tax schedule. The test is ex- pressed in reduced form and can be applied if the income distribution and empirical estimates of the extensive and intensive labor supply elasticities are known. Carefully parameterized simulations suggest that an EITC is optimal. An exogenous restriction that the welfare benefit cannot be set below a certain level causes the EITC to be less pronounced. On the other hand, exogenous government revenue requirements cause the EITC to be more pronounced in relative terms, because the welfare benefit decreases while the participation subsidy remains fairly constant. However, with the restriction of a fixed welfare benefit an increase in revenue requirements leads to a sharp decline of the participation subsidy.