In a number of high-income countries over the past few decades there has been a large growth in income inequality and at the same time a shift in the burden of taxation from the top to the middle of the income distribution. This paper applies the theory of optimal piecewise linear taxation to the issue of the taxation of top incomes. Our results suggest that an appropriate response to rising inequality is a shift towards a more progressive multi-bracket income tax system, with a more differentiated structure of rates in the top percentiles.