Medicare beneficiaries can buy Medicare Supplement Insurance, or Medigap, to help cover certain out- of-pocket costs associated with Medicare Part A and/or Part B. (If you’re shopping during open enrollment, through Dec. 7, remember that people with Medicare Advantage can’t buy Medigap plans.)

For example, depending on which plan type you choose, a Medigap policy could cover the 20% Medicare Part B coinsurance for office visits and the $1,600 deductible before Medicare Part A starts to pay for inpatient hospital care.

Medigap policies are sold by private health insurance companies. They’re regulated by the federal government and have certain standard benefits. But shopping for them isn’t always straightforward.

Shoppers might expect higher prices to come with more benefits, but that’s not always the case. Here are three scenarios to watch for so you don’t end up paying too much.

>> Paying more for the same coverage: New Medicare beneficiaries in most states can choose from up to eight out of 10 letter- named Medigap plan types: A, B, D, G, K, L, M and N. Each plan type offers a different set of benefits. (Medigap Plans C and F aren’t available to new Medicare members.)

“One of the most common and popular counseling tips we provide is that all plans of the same letter, i.e., A, B, C, D, are exactly the same. So there is no reason to pay more for one Plan A, B, C, D, over another,” Maureen McIntyre, CEO of Connecticut’s North Central Area Agency on Aging, which offers free Medicare counseling for local residents, wrote in an email.

It’s worth comparing quotes for the plan type you want. Companies might differ in terms of customer service and minor non- Medicare perks, but there’s no additional coverage to gain from buying a more expensive Plan G policy when a cheaper one is available, for example.

>> Paying more for less coverage: Of the eight standard Medigap plan types available, Plan A has the most basic benefits, and Plan G is the most comprehensive.

One might expect Plan A to cost less than other plan types with more coverage. But sometimes lower-coverage plans are priced higher.

For example, for a 65- year-old female nonsmoker in Chicago, Cigna quotes monthly premiums of $152.06 for Medigap Plan G and $169.33 for Medigap Plan A, with identical discounts built into both rates. The lower-coverage option (Plan A) costs $17.27 more per month.

“While it is not typical for Plan A plans to be rated higher than Plan G, we recognize that this can sometimes happen, due to the actuarial experience and cost relativities related to those plans,” a Cigna spokesperson wrote in an email.

Plan A might have higher premiums if the insurance company expects members with Plan A to have more expensive claims, even though Plan G has more coverage, according to the spokesperson.

Representatives for State Farm, Mutual of Omaha and Blue Cross and Blue Shield of Texas offered similar explanations for instances when their quotes showed Plan A priced higher than Plan G.

When you’re shopping, your own budget is what matters, so compare prices carefully to find the most cost-effective option.

>> Paying too much for add-ons: Some companies offer add-ons for purchase with their Medigap plans. For example, UnitedHealthcare’s “wellness extras” packages include access to a 24/7 nurse line, vision, hearing and dental discounts and a gym membership. (In some locations these perks are included at no additional cost.)

Sometimes adding these packages might have unexpected effects on the price of the plan.

For example, here’s what it costs to add UnitedHealthcare’s wellness extras — the same package — to two plans for a 65-year-old female nonsmoker in Dallas:

Plan G add-on cost is $6.62 per month ($133.22 for the base plan, $139.84 with extras).

Add the same package to Plan A, however, and it will cost an additional $174.80 per month ($130.81 for the base plan, $305.61 with extras).

These extras might be compelling with Plan G, but the drastically higher price to add the same perks to Plan A is a much worse deal.

On the other hand, there are also scenarios when add-ons make the whole package cheaper.

In Columbus, Ohio, UnitedHealthcare quotes $91.71 per month for Medigap Plan A for a 65-year-old female nonsmoker. But Plan A with wellness extras costs $87.23 — $4.48 cheaper. Even if you never use any of the extras, Plan A with the add-ons would still be a better deal than the option without them.