Last year, the administration reduced Medicare benefits by a small amount. Now, it wants to cut as much as $6 billion from the cost of Medicare, starting next October.

These moves are raising the cost of medical care, both for elderly patients and for the families who often help support them.

To cover these rising medical bills, more families are turning to private health insurance -- some of which is not very good. Thanks to a new federal program, certain kinds of private policies have been much improved. But to get the benefit of the new rules, you have to know what you're looking for -- and what you're not looking for.

You are not looking for a dread-disease policy like cancer insurance, or for a policy that pays $25 or $40 a day while you're in the hospital. In most cases, these policies offer insufficient protection from high medical bills, and the new federal rules do not improve them.

Instead, you are looking for an insurance policy specifically designed to cover many of the expenses not covered by Medicare. At the behest of Sen. Max S. Baucus (D-Mont.), Congress passed a bill permitting individual insurance companies to get a federal seal of approval for their policies if the laws in their states did not require certain minimum standards of coverage.

As a result, 46 states now have laws setting acceptable minimum standards for Medicare-supplement, or Medigap, policies. "This has improved the quality of some Medigap policies," James Hunt, director of the National Insurance Consumer Organization, told my associate, Virgina Wilson. "For example, it caused the American Association of Retired Persons to revise its offerings."

Of the four states that don't meet federal standards (Mass., N.Y., R.I. and Wyo.), Rhode Island deviates the most. New York and Massachusetts have higher standards in some areas but lower standards in others. In these four states, health insurers can apply for the federal seal of approval, to show that they meet minimum national standards even if their competition does not. Insurance buyers in those states should ask to see the federal seal.

In any state, a federally approved Medigap policy is required to meet the minimum standards listed below. You'll find that many policies exceed the standards (and charge a higher price). The basic rules:

1. At the very least, Medigap insurance must pay the expenses not covered by Medicare during the 61st to 90th day you're in the hospital (currently $65 a day); also, the expense not covered during the 60 "lifetime reserve" days that apply to long illnesses ($130 a day); also, 90 percent of your eligible hospital expenses, for 365 days after Medicare runs out.

(Note that Medicare pays for the first 60 days you're in the hospital except for a $260 deductible. This covers the vast majority of illnesses.)

2. Medigap insurance must pay the 20 percent of approved doctors' bills and other expenses not covered under Medicare, Part B. However, the policy can require you to pay the first $200 of expenses every year.

3. Your policy can exclude coverage for illnesses you already have, but only for the first six months. After that, pre-existing illnesses must be fully covered.

4. Applicants for Medigap insurance must receive a buyers' guide. If you change your mind about buying the policy within 30 days, the seller must refund your premiums.

5. The policy must be fairly priced. On individual policies, at least 60 percent of the premiums collected from all customers must be used to pay health benefits. Many group policies have to pay out at least 75 percent. This prevents sellers from setting prices too high.

But remember: This rule applies only to Medigap insurance. Cancer policies and daily-hospital-income policies may still be overpriced, relative to benefits received.

Certain group policies are excluded from the federal rules. So before joining an organization in order to get its Medigap policy, be sure you check its coverage against the above list of minimum standards.

One important note: the rules cover only newly sold Medigap policies, not old ones. If your present policy is below standard -- and many are -- you are not protected. Ask your insurance agent for a new policy, or shop for one from another company