We evaluate the effectiveness of a more progressive tax scheme in raising government revenues. We develop a life-cycle economy with heterogeneity and endogenous labor supply. Households face a progressive income tax schedule, mimicking the Federal Income tax, and flat-rate taxes that capture payroll, state and local taxes and the corporate income tax. We parameterize this model to reproduce aggregate and cross-sectional observations for the U.S. economy, including the shares of labor income for top earners. We find that a tilt of the Federal income tax schedule towards high earners leads to small increases in revenues which are maximized at an effective marginal tax rate of about 36.9% for the richest 5% of households – in contrast to a 21.7% marginal rate in the benchmark economy. Maximized revenue from Federal income taxes is only 8.4% higher than it is in the benchmark economy, while revenues from all sources increase only by about 1.6%. The room for higher revenues from more progressive taxes is even lower when average taxes are higher to start with. We conclude that these policy recommendations are misguided if the aim is to exclusively raise government revenue.