We propose a canonical model of optimal nonlinear redistributive taxation with matching unemployment. In our model, agents are endowed with different skill levels and labor markets are perfectly segmented by skill. The government only observes negotiated wages. More progressive taxation leads to wage moderation that boosts labor demand. We design the optimal nonlinear redistributive tax schedule in the absence of welfare benefits and extensive labor supply margin. Compared to their efficient values, at the optimum gross wages and unemployment are lower. Average tax rates are moreover increasing in wages. The robustness of these properties is also discussed.