What is the optimal shape of the income tax schedule? This paper compares the optimal (Mirrlees) tax and transfer policy to various simple parametric (Ramsey) alternatives. The environment features distinct roles for public and private insurance. We explore a flexible class of social welfare functions, one special case of which captures the taste for redistribution reflected in the current tax system. Optimal marginal tax rates increase in income in our baseline calibration to the United States, and the optimal tax schedule can be well approximated by a simple two parameter function. We show that the shape of the optimal schedule is sensitive to the amount of fiscal pressure the government faces to raise revenue. As fiscal pressure increases, the optimal schedule becomes first flatter, and then U-shaped, reconciling various findings in the literature.