“There wasn’t any pushback,” Mr. Skoda said. Haro’s employees are generally young and healthy, he said, and they rarely go to the doctor. Instead, they want to make sure they have adequate coverage if they go to the emergency room.

The company’s premiums average $433 a month, Mr. Skoda said, with employees paying one-fourth of the expense. A few employees opted for more traditional coverage, enabling them to go where they please. But they are paying significantly higher deductibles and out-of-pocket costs that could add thousands of dollars to their medical bills.

The last time health insurers and employers sought to sharply limit patients’ choice was back in the early 1990s, when insurers tried to reinvent themselves by embracing managed care. Instead of just paying doctor and hospital bills, insurers also assumed a greater role in their customers’ medical care by restricting what specialists they could see or which hospitals they could go to.

“Back in the H.M.O. days, it was tight networks, and it did save money,” said Ken Goulet, an executive vice president at WellPoint, one of the nation’s largest private health insurers, which is experimenting with re-introducing the idea in California.

The concept was largely abandoned after the consumer backlash persuaded both employers and health plans that Americans were simply not willing to sacrifice choice. Prominent officials like Mr. Obama and Hillary Rodham Clinton learned to utter the word “choice” at every turn as advocates of overhauling the system.

But choice  or at least choice that will not cost you  is likely to be increasingly scarce as health insurers and employers scramble to find ways of keep premiums from becoming unaffordable. Aetna, Cigna, the UnitedHealth Group and WellPoint are all trying out plans with limited networks.

The size of these networks is typically much smaller than traditional plans. In New York, for example, Aetna offers a narrow-network plan that has about half the doctors and two-thirds of the hospitals the insurer typically offers. People enrolled in this plan are covered only if they go to a doctor or hospital within the network, but insurers are also experimenting with plans that allow a patient to see someone outside the network but pay much more than they would in a traditional plan offering out-of-network benefits.