We prove a median voter theorem for monotonic reforms of non-linear tax systems and characterize reforms that are preferred by a majority of voters. There is a discontinuity: For incomes below the median, lowering marginal tax rates is politically feasible. For incomes above the median, higher marginal tax rates are politically feasible. We also derive a diagnosis system for reforms that are not only politically feasible but also welfare-improving. For instance, starting from laissez faire, higher taxes on the rich are both politically feasible and welfare-improving. Lower taxes on the poor, while politically feasible, are not welfare-improving.