Medigap plans, which work with traditional Medicare to cover deductibles and co-pays, come in 12 standardized versions, which makes it relatively easy to compare one with another by price. They often cost more than private Medicare plans, but they might be your best choice if you have a pre-existing condition. That's because if you sign up for a private Medicare plan and stay on it for a year or more, in all but a few states you give up your right to go back into a Medigap plan without consideration of a pre-existing condition. So the Medigap plan can refuse to take you, charge you extra, or even exclude coverage of your pre-existing condition. If you are healthy now but develop a health problem while in a private Medicare plan, you will not easily be able to go back to public Medicare plus Medigap, although you can switch to a different private plan. Only you can determine whether the immediate savings are worth the gamble.

Beware of private fee-for-service plans

This is the fastest-growing type of private Medicare plan, presumably because at first glance it seems to have the advantages of public Medicare but costs less. You can choose any doctor or hospital. But there's a catch: Many providers who accept patients with public Medicare are turning down patients in these plans. "The billing is often terrible—doctors wait months to be paid," Precht says. Also, people in these plans can end up having to pay large medical bills out of their own pockets if they don't contact their plans before obtaining treatment. Partly for those reasons, people leave those plans at more than twice the rate of other types of private Medicare plans, according to a recent study by the Government Accountability Office.

Find out whether you are entitled to extra government help

If your income meets certain guidelines (they vary by state), you might qualify for help with paying all or part of your Medicare costs, including help with your Part D drug plan. Your State Health Insurance Assistance Program, a free Medicare-Medicaid counseling service, can help you determine your eligibility. Find your state's program.