Morningstar analyzed 11 providers that make accounts available to individual savers, covering about 60 percent of the market. (The review didn’t include accounts offered through employers, since fees for workplace accounts vary widely, making comparisons difficult.) Over all, account fees have decreased and investment options have improved, the report found. But some H.S.A. providers still make it hard to find relevant details on their websites, like the interest rates paid on accounts.

Even though the accounts offer the potential for long-term investment, the vast majority of H.S.A. holders use the funds to pay current medical costs and hold the money in cash spending accounts. Just 4 percent of all accounts, or about one million, have at least part of the money invested, according to the H.S.A. services firm Devenir.

Some people may not invest because they don’t know they have the option, said Roy Ramthun, an H.S.A. consultant. He said people continue to confuse H.S.A.s with flexible health spending accounts, which aren’t portable and generally must be used before a deadline.

Another likely reason, however, is that H.S.A. holders need the funds to pay for ongoing medical costs, said Leo Acheson, associate director of multiasset and alternative strategies at Morningstar.

“A lot of people don’t have the financial means to set aside money for the future,” he said.

People who need to use their H.S.A. money now, Mr. Acheson said, should look for accounts with no or low maintenance and add-on fees, reasonable interest rates and Federal Deposit Insurance Corporation insurance. Morningstar’s top individual accounts for spenders, based on those criteria, include Fidelity, a relative newcomer to retail H.S.A.s; Lively, a start-up; and the H.S.A. Authority.