A group of prominent addiction doctors has mounted a quiet legal campaign on behalf of Cameron Douglas, the troubled son of the actor Michael Douglas, in hopes of finding a sympathetic ear for their view that drug addiction is best handled with more treatment, not more prison time.

In December, Mr. Douglas, who is 33 and already serving a five-year federal sentence for drug distribution and heroin possession, was sentenced to an additional four and a half years after being caught behind bars with heroin and Suboxone, a prescription medication used to blunt the pull of opioid addiction.

And it was that sentence, believed to be one of the harshest ever handed down by a federal judge for drug possession for an incarcerated prisoner, that prompted about two dozen addiction doctors and groups to file a brief on behalf of Mr. Douglas, whose case is under review by a panel from the United States Court of Appeals for the Second Circuit.

Their argument is that Mr. Douglas, who began injecting heroin daily in his mid-20s, is a textbook example “of someone suffering from untreated opioid dependence” and that more prison time would do nothing to solve his underlying problems.