Workers saw a modest rise in the average cost of employer-sponsored health insurance this year, but they're probably not overwhelmed with relief.

Coverage costs still are climbing faster than wages. That means, in many cases, a bigger portion of the average paycheck is sliced off for insurance instead of being deposited into employee bank accounts.

Annual premiums for employer-sponsored family coverage climbed nearly 4 percent this year to top $16,000 for the first time, according to a survey the Kaiser Family Foundation released Tuesday.

The cost of single coverage rose almost 5 percent compared with 2012. Those are smaller increases than the spikes of 9 percent for family coverage and 8 percent for single coverage recorded in 2011. But this year's increases lap a 1.8 percent rise in worker wages over the same period.

Plus, more companies are giving their employees coverage with a higher deductible, which requires a patient to pay more out of pocket for things like blood tests or MRIs before coverage starts. Coupled with the growing cost of coverage, that means some employees may be paying more for insurance that covers less.

While health care costs have generally grown more moderately since the Great Recession eased, the average worker still feels the pain of paying more, said Drew Altman, CEO of the nonprofit Kaiser Family Foundation, which conducts the survey on coverage costs with the Health Research and Educational Trust.

"Their costs are going up, their cost-sharing is going up, wages are flat and inflation is much lower," Altman said.

Employer-sponsored health insurance is the most common form of coverage in the United States. Employers typically cover most of the health insurance bill for their workers, and the actual change a worker sees in health insurance costs can vary greatly.

Some employers absorb cost hikes for their workers. Rate changes also depend on where the employee lives, the coverage he or she has and the size of the employer. Employees of smaller companies tend to see bigger cost fluctuations in part because those businesses have less leverage for rate negotiations.

Smaller employers also are turning more to high-deductible plans to help control insurance cost growth. These plans can cost less for the employer and shift more of the expense to the employee.

More than half of companies with fewer than 200 employees offered insurance with an annual deductible of $1,000 or greater this year for single coverage.