A growing number of U.S. workers are covered by health insurance that sticks them with a bigger share of the medical bill but also softens that blow by providing a special account to help with the expense.

Companies are turning more to these so-called consumer-directed health plans, which push patients to shop around for the best prices for care, because they can cost less than other types of coverage and help hold down future increases.

Nearly 3 out of 10 employees have this kind of coverage, up from 2 out of 10 in 2014, according to an annual study of private insurance trends from the Kaiser Family Foundation released Wednesday.

A decade ago, these plans were almost unheard of. In them, patients and employers generally pay less toward the premium, or cost of the coverage itself. But then patients have to pay higher amounts out of their own pockets for most care, up to a certain level known as the deductible. The idea is that customers will make smart financial decisions because more of their own money is on the line.

To help patients deal with potentially higher out-of-pocket costs — and entice workers to sign on to the plans — employers often set up an account and stock it with money that can be used to cover these expenses.

“Most employers want to continue offering insurance but they just want to pay less,” said Dan Mendelson, president of the consulting firm Avalere Health.

Mendelson, who reviewed the Kaiser study, said insurers have developed better tools for helping people compare cost and quality. That might make companies more comfortable with sending their employees out to shop for something as complicated as health care.

Kaiser researchers say rising deductibles from plans like this are helping to restrain premiums.

Overall, the cost of employer-sponsored health insurance, the most common type of coverage in the country, is still growing modestly like it has for the past five years, according to Kaiser. The average annual premium for family coverage, shared by employer and worker, rose 3 percent this year to $18,142. That’s more than double what coverage cost in 1999, even after adjusting for inflation.

Kaiser released its survey while companies are preparing to tell their employees about coverage options for next year. The annual window in which employees can enroll in their company’s insurance for 2017 or make changes to their coverage begins in November for many companies.

Here are some other highlights from the survey, which Kaiser conducted with the Health Research and Educational Trust.

— Despite modest increases in recent years, health insurance costs are still climbing faster than wages and inflation for many plans. Family coverage premiums have climbed a total of 20 percent over the last five years, while worker earnings have risen 11 percent and inflation has climbed 6 percent, Kaiser reported. This means that employers may be holding back on raises because they have to spend more on health insurance for each worker.

— Employers still pick up most of the bill for coverage. Workers paid, on average, 18 percent of the premium for individual coverage and 30 percent for family coverage. That’s the amount usually taken out of a paycheck before taxes.

— Deductibles are on the rise for many types of coverage. For the first time, the survey found that more than half of all covered workers face deductibles of at least $1,000 a year for individual coverage.

— The benefits consultant Mercer found in a separate survey that employers expect insurance costs to rise about 4 percent next year. That’s after employers make adjustments like raising deductibles or shopping for a new insurer for better prices.