In this article, we challenge the common thought that a liquidannuity contract is optimal. We indeed show, in a standard neoclassical framework, that another contract, which actually resembles much more to the contracts that are proposed by most insurance companies, may be preferred by rational individuals. According to this contract, the annuities are an illiquid asset and the premium is age independent. In an overlapping-generation economy, we show that liquid annuities are preferred only if the equilibrium is dynamically inefficient. Alternatively, an equilibrium displaying a positive demand for illiquid annuities is efficient. We conclude by showing how to implement an illiquid annuities market in an efficient economy.