Existing tax schedules are often overly complex and characterized by discontinuities in the marginal tax burden. In this paper we propose a class of progressive smooth functions to replace personal income tax schedules. These functions depend only on three meaningful parameters, and avoid the drawbacks of defining tax schedules through various tax brackets. Based on representative micro data, we derive revenue-neutral parameters for four different types of tax regimes (Austria, Germany, Hungary and Spain). We then analyze possible implications from a hypothetical switch to smoother income tax tariffs. We find that smooth tax functions eliminate the most extreme cases of bracket creep, while the impact on income inequality is mostly negligible, but uniformly reducing.