This paper analyzes the effects of lump-sum tax policy in an overlapping generations model in which consumers have uncertain longevity. It extends previous analyses by considering the case in which private insurance arrangements are actuarially unfair. In addition, it considers the polar case of actuarially fair insurance and the polar case of no insurance. A general condition for debt neutrality is derived. This condition depends explicitly on the degree of actuarial unfairness in insurance and on the extent to which parents care about the utility of their children.