In Oregon, the number of men and women who have died that way is roughly equal, and their median age is 71. Eighty-one percent have had cancer, and 7 percent A.L.S., which is also known as Lou Gehrig’s disease. The rest have had a variety of illnesses, including lung and heart disease. The statistics are similar in Washington.

There were fears of a “slippery slope” — that the law would gradually expand to include those with nonterminal illnesses or that it would permit physicians to take a more active role in the dying process itself. But those worries have not been borne out, experts say.

Dr. Wesley, a pulmonologist and critical care physician, voted for the initiative when it was on the ballot in 2008, two years after he retired. “All my career, I believed that whatever makes people comfortable at the end of their lives is their own choice to make,” he said.

But Dr. Wesley had no idea that his vote would soon become intensely personal.

In the months before the vote, he started having trouble lifting weights in the gym. He also noticed a hollow between his left thumb and index finger where muscle should be. A month after casting his vote, he received a diagnosis of A.L.S. Patients with the disease typically live no more than four years after the onset of symptoms, but the amount of time left to them can vary widely.

In the summer of 2010, after a bout of pneumonia and with doctors agreeing that he most likely had only six months to live, Dr. Wesley got his prescription for barbiturates. But he has not used them, and the progression of his disease has slowed, although he now sits in a wheelchair that he cannot operate. He has lost the use of his limbs and, as the muscles around his lungs weaken, he relies increasingly on a respirator. His speech is clear, but finding the air with which to talk is a struggle. Yet he has seized life. He takes classes in international politics at the University of Washington and savors time with his wife and four grown children.

In both Oregon and Washington, the law is rigorous in determining who is eligible to receive the drugs. Two physicians must confirm that a patient has six months or less to live. And the request for the drugs must be made twice, 15 days apart, before they are handed out. They must be self-administered, which creates a special challenge for people with A.L.S.

Dr. Wesley said he would find a way to meet that requirement, perhaps by tipping a cup into his feeding tube.