Q. Let's take an example of an older married couple, in their early sixties, on employer-sponsored health care insurance. How should they be thinking about Medicare?

A. First, make sure you understand when to sign up, so you avoid late-enrollment penalties. They are horrible and can be very damaging, and they last literally forever. Another reason why it's important to sign up on time is that you don't want to find yourself without coverage because you're late in enrolling. That's the more serious consequence. If, for example, you turn 65 and you're slow in signing up for Medicare, and your employer's policy ends your coverage and you have an adverse health event and no primary health insurance, you are in a world of hurt.

The traditional enrollment window for someone turning 65 is that you can enroll three months before your birthday month and three months after. But if your insurance with an employer ends during your birthday month (say, September) because you retire, it doesn't do you much good to wait to enroll until November—because you may avoid the late enrollment penalty, but if you get hit by a car you don't have any insurance. Your Medicare coverage will start on Jan. 1, in this example, and you will have a gap between coverage. Don't get too enamored of saving a dollar here or there by deferring enrollment until late in the enrollment period.

Also, there's no family plan with Medicare. A lot of couples get the same Medicare policies, even some otherwise very intelligent friends of mine. Life is easier when it's simpler. But it doesn't make sense unless their health profiles are identical. Q. What advice do you have for people who want to buy additional insurance to cover some of what Medicare doesn't?

A. When you sign up for Medicare, most people buy Part A, which covers hospital stays, and Part B, which covers doctors, outpatient and medical equipment expenses, and then decide on additional products.

Usually you need a Part D drug plan, and then there are two products—Medigap (or Medicare supplemental insurance, as it's also called) and Medicare Advantage plans. They are sold by private insurers and cover many of the expenses that basic or original Medicare does not. You buy one or the other. It's illegal for insurance companies to sell both of these to the same person, because they cover a lot of the same things.

Medicare Advantage also comes with Plan D rolled in. These are usually easier to use, because you have one insurance product you deal with for all your Medicare needs. But Medicare Advantage plans make their money by restricting policyholders' access to care by requiring them to use caregivers in the plan's provider networks. (I joke in the book that the letters HMO still cause shudders in marketing circles, but these plans are basically HMOs. Some are very good, though; Kaiser Permanente's plans have a great reputation.) Most affluent people don't take that route, because they want to use whatever health-care providers they need to take care of themselves and their loved ones. That's what you can do with basic Medicare. If you use Parts A and B, you can use whatever health-care provider in the U.S. works with Medicare, and almost all of them do. So wherever you are in the U.S., you can get health-care services. If you are traveling and you need a prescription, you can go into the local pharmacy and Medicare will fill it. That's often not the case with Medicare Advantage plans.

Q. What are other big trade-offs? A. Traditional Medicare has great flexibility but large coverage gaps. Plan B pays only 80 percent of covered expenses. You pay 20 percent, and there's no annual ceiling. You can largely close that big hole by buying a Medigap plan. There are 10 different so-called letter plans that you can buy.

With Medigap, the policies are regulated by the states, but what they cover is dictated by Medicare. The most popular Medigap plan is F, which covers the most, and the C plan is second. If you have F, regardless of where you are in U.S., every F plan has to cover same thing, because federal rules dictate what that plan and all the other letter plans cover.

The only real variation in Medigap plans is the premium—and there is an enormous range.