If you have Part A and Part B of Medicare, you can buy a private insurance plan called a Medigap plan. The plan pays for deductibles and coinsurance that Part A and Part B do not cover, like health care you may need when traveling outside the U.S.. There is a 6 month open enrollment period that begins after you turn 65 and enroll in Part B. During that enrollment time, you cannot be denied a Medigap policy from any company that sells them in your area. Once you have a Medigap policy, your insurer must let you re-enroll every year – they cannot drop you. If you try to buy a Medigap policy outside the open enrollment period, insurers do not have to offer one to you.