In this paper, we consider illiquid life annuity contracts and show that they may be preferred to those illustrated by Yaari. In an overlapping generations economy, liquid life annuities are demanded only if the equilibrium is dynamically inefficient. However, an equilibrium displaying a positive demand for illiquid life annuities is indeed efficient. In this latter case, the welfare at steady state is larger if illiquid life annuity contracts are available.