— NEW YORK — A chastened Jayson Williams admitted Friday he was driving drunk when he slammed his SUV into a tree, capping years of legal and personal problems with a guilty plea that adds more time behind bars for the already imprisoned former NBA star.

His voice sometimes unsteady, Williams apologized to his family and said he was working to rebuild his life as he pleaded guilty to driving while intoxicated in the Jan. 5 crash.

His one-year sentence — the maximum for the misdemeanor offense — will follow the five-year prison term he’s serving in New Jersey for accidentally shooting and killing a limo driver.

“It seems excessive, but it’s a small price to pay if it helps to deter drunk driving,” Williams, 42, said in a Manhattan court. “I’ll be the poster child for that if it’s going to save lives.”

“I’m doing the best I can in New Jersey so this will never happen again,” added Williams, dressed in a tan inmate uniform. He nodded to supporters, including his frail mother, before being led out of court.

The former New Jersey Net was a top player with a six-year, $86 million contract before a leg injury forced him to retire in 2000. A first-round NBA draft pick in 1990, he played nine seasons with the Philadelphia 76ers and the Nets. He averaged 10 or more rebounds a game in his final four NBA seasons and was named to an All-Star team.

Two years after retiring, he killed chauffeur Costas Christofi with a 12-gauge shotgun while showing it to friends, having failed to check the weapon’s safety mechanism. Williams then wiped down the weapon and placed it in Christofi’s hands, stripped off his own clothes, handed them to a friend and jumped into his pool, according to testimony. Williams’ lawyers said his actions were driven by panic.

The shooting marked the start of a cascade of troubles for Williams, who was promptly suspended from his post-basketball job as an NBA analyst for NBC.

While the case surrounding the shooting lingered after a 2004 mistrial on a top count, his wife filed for divorce last year, and police used a stun gun on him in a New York hotel after a female friend said he was acting suicidal.

He was charged with assault in May 2009 after allegedly punching a man in the face outside a North Carolina bar, but charges were dropped.

In November, Williams’ father, E.J., with whom he owned a construction business, died in South Carolina.

The SUV wreck happened the week before Williams pleaded guilty in New Jersey to aggravated assault in Christofi’s death. He began serving his prison term in February and is making progress in counseling, alcohol-abuse, problem-solving and leadership programs, said his lawyer, Oscar Holt III.

“His life spiraled downward, but it’s now back on the rise,” Holt said. He said Williams was disappointed in the sentence but relieved to put the case behind him.

Also disappointed was Williams’ estranged wife, Tanya Young Williams, who wasn’t in court and said she learned of his decision to plead guilty only afterward — with no time to prepare their daughters, 6 and 7, for the news.

“It’s going to be tough for them to understand another year,” she said by telephone. “Every time he’s in the news for something, it does affect my family. ... I pray that he gets back to whoever that person was before all the chaos took over his life.”

Williams had a blood-alcohol level more than twice the legal limit when he was taken to a hospital after his SUV hurtled off a highway exit ramp and across a street near Manhattan’s East Village around 3 a.m., prosecutors said.

“He came within seconds of striking a car that was pulled up to a traffic light,” Assistant District Attorney William Beesch said.

Police found him sitting in the passenger seat. He told them someone else was driving and had left, but prosecutors said surveillance video and witnesses established he had been alone in the car.

Many first-time DWI offenders don’t get jail time. Holt urged Criminal Court Judge Rita Mella to disregard prosecutors’ push for the maximum penalty for Williams, saying his client was committed to sobriety and will serve as an effective advocate against drinking and driving.

Mella said she was “considering all the factors that I must in this case” as she imposed the one-year jail term — and ordered Williams to pay the city more than $16,600 for replacing the tree.

If he’s granted parole in New Jersey and then gets time off for good behavior in New York, Williams could end up paring his total time behind bars to a little over two years.

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AP Sports Writer Dan Gelston contributed to this report from Philadelphia.