Some gravely ill alcoholics who need a liver transplant shouldn’t have to prove they can stay sober for six months to get one, doctors say in a study that could intensify the debate over whether those who destroy their organs by drinking deserve new ones.

In the small French study, the vast majority of the patients who got a liver without the wait stopped drinking after their surgery and were sober years later. The study involved patients who were suffering from alcohol-related hepatitis so severe that they were unlikely to survive a six-month delay.

The findings, reported in Thursday’s New England Journal of Medicine, could boost demand for livers, already in scarce supply, and reopen a bitter dispute over whether alcoholics should even get transplants.

The controversy peaked in the 1990s when celebrities with drinking problems — Larry Hagman, David Crosby and Mickey Mantle — got liver transplants.

Alcohol can cause lethal, liver-destroying diseases such as cirrhosis and hepatitis. Nearly one in five liver transplants in the U.S. go to current or former heavy drinkers. Transplant hospitals commonly require patients waiting for a new liver to give up drinking for six months as a way of assuring doctors they are serious about staying sober after the operation.

Drinkers severely ill with hepatitis account for a very small share of patients needing transplants. The French study suggests that dropping the six-month rule would increase demand for livers by only about 3 percent.

The study’s lead author said a strict application of the six-month rule may be unfair to such patients. He said they are just as deserving as other liver patients, many of whom have diseases caused by poor lifestyle choices such as drug use or obesity.