This paper uses a heterogeneous‐agent overlapping‐generations model to examine the fiscal and distributional consequences of introducing a means test in US Social Security. I find that a means test, that is, conditioning benefit payments on a household's earnings or assets, leads to a higher implicit tax on old‐age resources, but has desirable distributional effects. A 75% cut in the benefits to households with earnings of more than 200% of the median leads to a 2.3% reduction in the overall size of Social Security, but has almost no effect on average dollar benefits. In contrast, a fiscally comparable payroll tax cut leads to an across‐the‐board decline of 2% in the average dollar benefits, despite an increase in capital and labor. A fiscally comparable delay in the benefit eligibility age increases benefits for all, but negatively affects capital and labor. Finally, an asset‐based means test causes a decline of 1% in the average dollar benefits, but has a large negative effect on capital and the accidental bequests left behind by deceased households.