NEW YORK (CNNMoney) -- Health insurance premiums rose a modest 4% in 2013, but that's still more than twice the rate of workers' wages.
Workers are shelling out an average of $4,565 for their employer-sponsored family health coverage this year, according to the annual survey conducted by the Kaiser Family Foundation and the Health Research & Educational Trust. That's still only 28% of the total price of $16,351.
Premiums for individual plans rose 5% to a total of $5,884, of which employees paid an average of $999, according to the survey, released Tuesday.
While health insurance costs have been rising more slowly in recent years, so have wages. Workers saw their incomes rise by only 1.8%.
Over the past decade, employee premiums have risen 89%, nearly three times as fast as wages.
Still, this year's increase was the second lowest premium increase since Kaiser/HRET began conducting the survey in 1999. A decade ago, increases of more than 9% a year were common.
"We are in a prolonged period of moderation in premiums, which should create some breathing room for the private sector to try to reduce costs without cutting back benefits for workers," said Drew Altman, Kaiser's chief executive.
But companies are still passing along more costs to workers. About 78% of all covered workers face an annual deductible, up from 72% last year. The average deductible for single coverage rose only a tiny bit to $1,135 since 2012, but the change in recent years is more pronounced. In 2009, the annual deductible was only $826.
Employers are also trying to control costs by offering wellness programs. Some 26% of large firms with more than 200 workers and 10% of smaller firms have a wellness program, with the most popular being flu shots and vaccinations.
Health insurance costs and availability vary widely by size of firm and share of low-wage workers within the company.
Among companies with 50 or more workers, 93% offer health benefits. Firms of this size will have to provide affordable insurance to workers starting in 2015, under the Affordable Care Act.
Only 57% of smaller firms provide their workers with health insurance. Workers at smaller firms also have to pay more for family coverage than their peers at bigger employers, though they contribute less for individual insurance.
How many low-wage workers are employed at a company also affects premiums levels. The Kaiser study found that employees had to contribute $5,818 at firms with many low wage workers, as opposed to $4,030 at firms with higher-paid staff. The employer contribution at firms with lower-paid workers was also smaller.