All individuals face some risk of ending up old, sick, alone and poor. Is there a role for social insurance for these risks and, if so, what is a good program? A large literature has analyzed the costs and benefits of pay-as-you-go public pensions and found that the costs exceed the benefits. This paper, instead, considers means-tested social insurance programs for retirees such as Medicaid and Supplemental Security Income. We find that the welfare gains from these programs are large. Moreover, the current scale of means-tested social insurance in the U.S. is too small in the following sense. If we condition on the current Social Security program, increasing the scale of means-tested social insurance by 1/3 benefits both the poor and the affluent when a payroll tax is used to fund the increase.