This paper presents a reform of the structure of the Italian personal income tax (IRPEF) which combines a plurality of objectives: simplifying the tax and smoothing the curves of the tax rates; increasing the transparency and comprehensibility of the tax for the taxpayer; providing tax authorities with a tool that can be used for purposes of redistribution in a simple and effective way. A tax function radically different from the current one is proposed, moving from the progressivity by marginal tax rates/income brackets to a continuous average tax rate schedule. Specifically, the curve of the average tax rates is derived by imposing constant elasticity of the after-tax income (residual income progression) for a large range of taxable incomes. The paper presents some tentative simulations of the effects of this reform on tax yield and redistribution based on tax returns data in 2018.