As policymakers look for savings from the Medicare program, some have proposed eliminating or discouraging “first-dollar coverage” available through privately purchased Medigap policies. Medigap coverage, which beneficiaries obtain to protect themselves from Medicare’s cost-sharing requirements and its lack of a cap on out-of-pocket spending, may discourage the judicious use of medical services by reducing or eliminating beneficiary cost sharing. It is estimated that eliminating such coverage, which has been shown to be associated with higher Medicare spending, and requiring some cost sharing would encourage beneficiaries to reduce their service use and thus reduce program spending. However, eliminating first-dollar coverage could cause some beneficiaries to incur higher spending or forego necessary services. Some policy proposals to eliminate first-dollar coverage would also modify Medicare’s cost sharing and add an out-of-pocket spending cap for fee-for-service Medicare. This paper discusses Medicare’s current cost-sharing requirements, Medigap insurance, and proposals to modify Medicare’s cost sharing and eliminate first-dollar coverage in Medigap plans. It reviews the evidence on the effects of first-dollar coverage on spending, some objections to eliminating first-dollar coverage, and results of research that has modeled the impact of eliminating first-dollar coverage, modifying Medicare’s cost-sharing requirements, and adding an out-of-pocket limit on beneficiaries’ spending.