Although demand for care appears to be growing relatively slowly, insurers and benefit consultants also say prices for medical care continue to climb as prescription drug makers and hospitals charge more. “If they’re a popular brand or anchor hospital, they’re going to negotiate a significant increase if they can,” said Edward A. Kaplan, a benefits expert with the Segal Company, which recently surveyed insurers about medical costs.

The question for employers and insurers is whether the lackluster economy, as well as recent efforts by employer and insurers to better manage the medical care of workers, will keep premiums increasing at a more moderate level. Early responses to a survey by Mercer, a consulting firm, suggest employers are expecting the cost of providing health benefits to go up about 5 percent next year, according to Beth Umland, Mercer’s director of research for health and benefits. These companies may be factoring in the more pessimistic view of the economy, she said, where any recovery seems further off than it did a few months ago.

Employers are reporting that their workers are using less medical care, said Ms. Umland, but they and insurers have been slow to estimate costs that reflect the lower demand. “It always takes a while for underwriting to catch up with reality,” she said.

Some small business say they expect their premiums to moderate, but only because of changes in their work force — partly caused by younger, healthier employees — that make it less likely that the companies will incur high medical claims. “Up until last year, we saw very hefty increases -- double digits,” said Heather Gombos, an executive for R. M. Jones & Company and affiliated businesses in New Britain, Conn. , a group that insures about 50 of its 80 employees.

Family coverage is now running $12,000 a year, Ms. Gombos said, and she is waiting to see what rate increases her insurer proposes for the coming year. She thinks premiums will not rise as sharply in 2012. “What it comes down to is we’ve had some good luck,” she said.

Some businesses say they anticipate relief from higher costs in the coming year for a variety of reasons. At Ogilvy & Mather, the New York advertising firm, the company believes its efforts to encourage wellness and better oversee its employees’ health through an on-site medical clinic are paying off. "We are not anticipating any cost increase for employer and employee," said Gerri Stone, the senior partner who oversees the firm’s benefits strategy.

Ms. Stone acknowledged that the firm’s 3,600 employees were relatively young and healthy, helping it avoid some of the sharp increases experienced by other businesses. "We’ve never gone into the double digits," she said. Family coverage runs about $16,000 a year, she said.