The authors analyze to what extent and how the tax burden should be shifted towards top income earners in order to reduce income inequality. Starting from Lambert and Aronson (Inequality decomposition analysis and the Gini coefficient revisited 1993) and Alvaredo (A note on the relationship between top income shares and the Gini coefficient 2011) decomposition by income groups, they prove that for three types of revenue-neutral linear personal income tax reforms (PIT) based on Pfähler (1984) the redistributive effect is always higher than before the reform; and when the size of the rich group is sufficiently small (e.g. 1%), the best option is allocating tax changes proportionally to net income, and the worst doing it proportionally to tax liabilities. An empirical illustration of the theoretical results is provided using micro data from the Spanish PIT.