Some political leaders have proposed to lower individual income tax rates and make up the lost revenue by eliminating tax preferences. To help inform the discussion of such proposals, we examine illustrative revenue-neutral combinations of lower rates and cuts in tax preferences and their effects on the distribution of tax burdens. We conclude that paying for lower rates would require substantial reductions in broadly-used and popular preferences. In addition, requiring that changes maintain the current progressivity of the federal income tax would make it much harder to find a politically acceptable mix of preferences to curtail.