With reimbursement, “I’d do one of these a day,” said Dr. Hinterberger, whose 3,000 patients in the Finger Lakes region range from college professors to Mennonite farmers who tie horse-and-buggies to his parking lot’s hitching post.

If Medicare covers end-of-life counseling, that could profoundly affect the American way of dying, experts said. But the impact would depend on how much doctors were paid, the allowed frequency of conversations, whether psychologists or other nonphysicians could conduct them, and whether the conversations must be in person or could include phone calls with long-distance family members. Paying for only one session and completion of advance directives would have limited value, experts said.

“This notion that somehow a single conversation and the completion of a document is really an important intervention to the outcome of care is, I think, a legal illusion,” said Dr. Diane E. Meier, director of the Center to Advance Palliative Care. “It has to be a series of recurring conversations over years.”

End-of-life planning remains controversial. After Sarah Palin’s “death panel” label killed efforts to include it in the Affordable Care Act in 2009, Medicare added it to a 2010 regulation, allowing the federal program to cover “voluntary advance care planning” in annual wellness visits. But bowing to political pressure, the Obama administration had Medicare rescind that portion of the regulation. In doing so, Medicare wrote that it had not considered the viewpoints of members of Congress and others who opposed it.

Politically, the issue was dead. But private insurers, often encouraged by doctors, began taking steps.

“We are seeing more insurers who are reimbursing for these important conversations,” said Susan Pisano, a spokeswoman for America’s Health Insurance Plans, a trade association. The industry, which usually uses Medicare billing codes, had created its own code under a system that allows that if Medicare does not have one, and more insurance companies are using it or covering the discussions in other ways.

This year, for example, Blue Cross Blue Shield of Michigan began paying an average of $35 per conversation, face to face or by phone, conducted by doctors, nurses, social workers and others. And Cambia Health Solutions, which covers 2.2 million patients in Idaho, Oregon, Utah and Washington, started a program including end-of-life conversations and training in conducting them.