The military taught Nelson Guzman to be a perfectionist — so he learned to roll the perfect joint.

Guzman, 31, spent eight years in the Marines. But after he got home to Brooklyn, he returned to a habit of smoking pot — something that landed him in jail when he was busted buying pot and cocaine last June.

A year later, he’s in rehab, and one of the about 100 people to pass through Brooklyn’s Veterans Treatment Court, a program specifically for vets caught in drug offenses.

The City Council meets Monday to consider a resolution urging Veterans Treatment Courts in every borough. The Brooklyn court, with about 35 veterans, has graduated three since it started last year — meaning they completed a year-long rehab process that ends with their charges being dismissed.

The court is designed to treat drug addiction as a disease, and rehab and social services are offered as an alternative to jail. Many veterans struggle with addiction after deployments, sometimes as a way to deal with the stress of war, or returning to a pre-service drug habit.

Friday, Judge Michael Brennan presided over several different hearings, starting out by asking the defendants to raise their hands: Were they from the Army, the Navy or the Air Force?

Guzman, a former Marine, was the third veteran called. After the Williamsburg native served from 2000 to 2008, he returned home, and picked back up a drug habit. In the meantime, the Army taught him to strive for perfection.

“I was a perfectionist of using drugs,” he said. “I smoked pot. I had the nicest rolled joint.”

After he was arrested, he went to treatment court, where the offer was jail or rehab. He chose rehab. In November, he relapsed — a drug test showed booze — and he started from scratch. Once he is sober for a year, his charges may be dismissed.

The treatment courts are focused on giving nonviolent, drug-abusing defendants access to drug treatment programs, instead of incarceration. In a typical criminal court, Brennan said, defendants may get one or two chances before being sent to jail.

In court, the judge walked down from the bench to congratulate Guzman after caseworkers described his sober success and pursuit for a degree in physical education focusing on special education. The judge and Guzman shared a salute.

“We don’t give up,” said the judge. “They have earned the special treatment with their service.”

A similar court in Queens offers treatment instead of incarceration to veterans who plead guilty to nonviolent crimes.

Judge Brennan is a Vietnam veteran himself. He said the veterans respect him in the courtroom because, “They can’t say to me, ‘How do you know what I went through?’”

Gladys Bradley, 46, in the U.S. Army from 1984 to 1987, was arrested in July 2011 when she said alcohol addiction slipped into a drug bust for buying cocaine.

She too said the military perfected her, for better or worse. “The military, they tell me, ‘Be all you can be,’” she said. “So I became the best alcoholic.”

Funneled into treatment court, she began in-patient treatment, and was sentenced to five days in Rikers Island when she left without permission.

That gave her time to think, she said. Now, she’s 11 months sober.

“My kids are so proud of me, and I’m so proud of me,” she said. “I couldn’t say that last year.”

Struggles with pride and shame

Margarita Fournier, a resource coordinator at the Brooklyn Treatment Court, said that veterans often feel embarrassed by their struggles, or too proud to admit them.

With a mentor that has gone through the same thing, “They feel like that’s something they can reach out to.”

Thomas Daley, who works at the Brooklyn Vet Center, added that it often takes time for veterans to realize how to handle what they’ve been through, and how it has affected their lives, perhaps in marriage or job difficulties.

“They just came from hell. They don’t realize the damage that’s done,” he said. “You get a little bottle because you can’t get to sleep. You have nightmares.”