In enhanced annuities, the annuity payment depends on one's state of health at some contracted date while in "standard annuities", it does not. The focus of this paper is on an annuity market where "standard" and enhanced annuities areoffered simultaneously. When all insured know equally well on their future health status either enhanced annuities drive standard annuities out of the market or vice versa. Both annuity types can exist simultaneously when the insured know varying exactly on their risk type. In the case of the existence of such an "interior" solution, its is derived that this solution must be unique in the case of risk averse insured and that it Pareto-dominates the corner solution. Finally, it is shown that in all cases where at least part of the insured buy enhanced annuities social welfare is reduced
