Many economies have recently adopted the defined-contribution retirement financing system, but one disadvantage of this system is that retirees have to bear longevity risk. As a result, several economies have also introduced the public annuity plans. We analyze the similarities and differences between voluntary public annuity with ceiling (VPAc) plan and mandatory public annuity with flexibility (MPAf) plan that are empirically observed. Introducing either plan reduces the severity of adverse selection in public annuities, but further distorts the private annuity market. These two plans have systematically different effects on retirees’ utility levels: the good health group is adversely affected and the average health group benefits. On the other hand, the poor health group benefits from the VPAc plan but may be adversely affected under the MPAf plan.