In fact, Aon forecasts a 4.1 percent increase for 2016. As with lending rates, though, several prognosticators have predicted higher plan increases for several years, and have consistently been proven wrong when the data was crunched.

But while the rate has slowed, the average amount that employees need to contribute toward their health care has increased more than 134 percent over the past decade.

According to Aon, employees contributed $2,490 toward the premium and another $2,208 in out-of-pocket costs, such as copayments, coinsurance and deductibles in 2015. In contrast, the amount of employees' premium and out-of-pocket costs combined in 2005 was just $2,001.

The total premium cost per employee now sits at $11,032.

The consulting firm concluded that employers will stick with cost-shifting and with encouraging employees to get coverage via high-deductible plans, and more will restrict coverage to employees rather than offering it to spouses and other dependents. Aon's research showed:

• 18 percent of companies have reduced subsidies for covered dependents, while 17 percent added a surcharge for adult dependents with access to other health coverage.

• 43 percent of companies are considering using unitized pricing — where employees pay per person and not individual versus family.

Aon said big companies are also using their clout to pursue the longer term strategy of paying for quality by gradually incentivizing employees to get their medical care through certain approved physicians and hospital systems. Among the trends cited:

• Steering participants (through plan design or lower cost) to high quality hospitals or physicians for specific procedures or conditions (22 percent);

• Offering value-based insurance design approaches (28 percent);

• Adopting reference-based pricing — where employers set a pricing cap on benefits for certain medical services for which wide cost variation exists with no discernible differentiation in quality (6 percent). Another 53 percent plan to do so in the next three-to-five years.

And to combat the current "bad guy" in the health cost equation — prescription drugs — "employers are adjusting pharmacy design components to encourage the use of generic drugs. This includes using coinsurance rather than copays for brand drugs and by introducing mandatory generic and step therapy programs."

The average size of the employers in the database is about 20,000 employees, representing $59 billion in 2015 health care spending, Aon said.