In enhanced annuities, the annuity payment depends on one's state ofhealth at some contracted date while in "standard annuities", it does not.The focus of this paper is on an annuity market where "standard" and en-hanced annuities are oered simultaneously. When all insured know equallywell on their future health status either enhanced annuities drive standardannuities out of the market or vice versa. Both annuity types can exist si-multaneously when the insured know varying exactly on their risk type. Inthe case of the existence of such an "interior" solution, its is derived that thissolution 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 whereat least part of the insured buy enhanced annuities social welfare is reduced....