WASHINGTON » It sounds like good news: Annual premiums for job-based family health plans went up only 4 percent this year.

But hang on to your wallets. Premiums averaged $15,745, with employees paying more than $4,300 of that, a glaring reminder that the nation’s problem of unaffordable medical care is anything but solved.

The annual employer survey by two major research groups also highlighted another disturbing trend: employees at companies with many low-wage workers pay more money for skimpier insurance than what their counterparts at upscale firms get.

Overall, “it’s historically a very moderate increase in premiums,” said Drew Altman, president of the Kaiser Family Foundation, which conducted the survey with the Health Research & Educational Trust.

He quickly added: “But even a moderate increase feels really big to workers when their wages are flat or falling.”

Last year’s 9 percent increase in premiums was fodder for the political debate, with Republicans blaming President Barack Obama’s health care law. However, Obama’s big push to cover the uninsured doesn’t get going until 2014, and his most significant cost-control measures take effect even later. Rising health care costs reflect underlying problems that have frustrated policymakers of both parties for years, not to mention corporate benefit managers.

The survey comes a week after a report from an arm of the National Academy of Sciences estimated that about 30 cents of every dollar spent on health care — $750 billion a year — is wasted through unnecessary procedures, cumbersome paperwork, uncoordinated care and fraud.

Obama says he’s working to make health care more affordable for all by leveraging the power of government programs like Medicare to pay hospitals and doctors for quality results, rather than sheer volume of tests and procedures. But that will take time.

Republican Mitt Romney wants to give future retirees a fixed amount of money to pick either private insurance or a government plan modeled on Medicare. He expects the private market will find ways to deliver quality service at lower cost. The GOP approach mirrors the shift away from traditional pensions, which pay a standard benefit, to 401(k) savings plans that limit the employer’s exposure.

The Kaiser/HRET survey found that employee-only coverage went up 3 percent this year, with annual premiums averaging $5,615. Companies usually pick up a larger share of the cost for employee-only coverage, so workers typically paid about $950 of that.

The rise in premiums easily outpaced workers’ raises and inflation.

Employer-based coverage, the mainstay for working people and their families, remained stable this year, with 61 percent of all companies offering health benefits. However, only half of companies with 3 to 9 workers offered health insurance, while virtually all large firms with 1,000 or more employees did so.

A trend toward shifting workers into plans with high annual deductibles seems to have slowed somewhat. The deductible is the amount you must pay each year before insurance kicks in. The survey found that 34 percent of workers are in plans with annual deductibles of at least $1,000 for single coverage, up from 31 percent in 2011.

“We don’t know if it’s a timeout, or if it’s reached some natural limit,” said Altman. “It’s really something to watch for in the future because (high deductible plans) have an impact both on people’s budgets and on holding down overall costs.”

The survey’s focus on health insurance provided to lower-wage workers highlights one of the major areas of uncertainty around Obama’s health care law.

If the president is reelected and the law goes into full effect, employers with lots of low-wage workers may be tempted to drop coverage and send their employees into new state-based insurance exchanges, markets that will offer taxpayer-subsidized private insurance. A separate survey this summer by the Mercer benefits consulting firm found that 9 percent of employers in the retail and hospitality industries say it’s likely they will drop coverage, even if they have to pay penalties to the government.

The survey found that workers in lower-wage companies pay $4,977 toward the cost of family coverage, as compared to an average of $4,316 for all workers. And the policy they get for their money is less generous, typically worth about $1,000 less.

“They are really paying more and getting less,” said Altman. “That may not be surprising, but it is a striking finding.”

Although employers and government are doubling down on efforts to keep health care costs manageable, most experts believe the sluggish economy provides the likeliest explanation for the moderate rise in premiums. Last year’s spike is being blamed on a mistaken bet by insurers that the economy would recover faster.

The survey includes more than 2,000 small and large employers. Asked what kind of increase they’re expecting for 2013, employers said their best estimate at this point is 7 percent.