Many Social Security reform proposals recommend increasing the age at which people become eligible for Social Security retirement benefits as a way to reduce future expenditures, maintain benefit adequacy in light of other benefit cuts, and increase labor supply. But the amount by which the benefit eligibility age is increased in reform plans is rarely chosen based upon principles of optimal social insurance. In this paper we analyze the question of the optimal eligibility age using two models of optimal social insurance. In the first model, the eligibility age exists because of a paternalistic concern that some people will mistakenly retire too early if left to make decisions on their own. In the second model, the eligibility age represents the age at which it is no longer cost effective to screen people for disability. We parameterize the models using new estimates of how the distribution of health status at each age has evolved in the U.S. over the past four decades.