Businessman Rodney Williams on Wednesday became the latest in a string of federal targets to get leniency in exchange for their help in putting former Mayor Ray Nagin behind bars.

U.S. District Judge Susie Morgan sentenced Williams, a former principal in the engineering firm Three Fold Consultants who admitted to bribing Nagin repeatedly, to a year and a day in prison. Williams had faced a maximum of 37 months under the terms of a December 2012 plea agreement that set the stage for Nagin’s indictment a month later.

Williams, 49, was the star witness in the government’s case against the former mayor, who began serving a 10-year prison sentence at a minimum-security federal camp in Texarkana, Texas, on Monday.

Morgan said she gave strong weight to Williams’ assistance in making the case against Nagin, but she said she could not allow him to avoid prison altogether, as his attorney had requested.

“Bribery of a public official, in this case Mayor Ray Nagin, is a serious offense, one that is particularly odious to the court and to the citizens of New Orleans,” she said.

Williams admitted in his guilty plea, and later on the witness stand, that he had bribed Nagin and his sons in exchange for the mayor’s help in securing no-bid city contracts as the city embarked on a massive rebuilding program after Hurricane Katrina.

He gave a tearful apology in court Wednesday, choking up repeatedly and pausing to collect himself as he sought to speak. He said he had let down his church, his city and, most importantly, his three children, now in young adulthood, who he said “were forced to mature before their time.” Williams’ wife died in 2007, before his legal troubles began.

“I’d like to apologize to the citizens of New Orleans for everything I’ve done and all the grief I’ve caused them,” he said. “I’m just sorry for all I’ve done ... and I pray people forgive me for it.”

Williams was crucial to the government’s case because he was the only key witness who was legally untainted save for his interactions with the mayor. He was thus the most credible of Nagin’s co-conspirators to testify.

He portrayed himself as a businessman unable to get much work from the city until he agreed, along with his two partners in Three Fold, to pump $60,000 into the Nagin family’s granite business, Stone Age. The partners did so with the understanding that the doors of City Hall would open to them, and soon, Three Fold was getting dozens of contracts, he testified.

The Nagins later created documents — which Williams said were bogus — that indicated the Three Fold partners shared a 4.5 percent ownership interest in Stone Age.

Williams, who dealt directly with Nagin, was the only one of Three Fold’s partners to be charged, though each partner put up $20,000 for the phony stake in Stone Age. Williams said he also ponied up another $12,250 in bribes to Nagin’s sons after the initial bribe.

Williams was the first witness for the government at Nagin’s trial, and his lawyer, Ralph Capitelli, described him Wednesday as a “leadoff batter” who “hit an inside-the-park home run.” He said Williams’ remorse, humility and truth contrasted sharply with Nagin’s “arrogance,” “rationalizations,” “political showmanship” and lies.”

Prosecutors had asked Morgan for leniency, and the judge granted a motion for a downward departure from the sentencing guidelines.

“We could not have done this case without the help of individuals like Rodney Williams,” Assistant U.S. Attorney Matt Coman told Morgan. “It was clear from the jury’s verdict that Mr. Williams’ testimony was truthful and impactful.”

Other witnesses in the case have also benefited from their cooperation with the government.

Last week, Nagin’s former chief technology officer, Greg Meffert, was sentenced to 30 months in prison, far less than the eight years that federal sentencing guidelines called for in his case.

The next day, technology vendor Mark St. Pierre — who also cooperated after his 2011 conviction for bribing Meffert but did not testify against Nagin — saw his 17 1/2-year sentence trimmed to five years as thanks for his help.

Another major witness in the case against Nagin was businessman Frank Fradella, who pleaded guilty to orchestrating a huge stock fraud as well as to bribing Nagin. Fradella is due to be sentenced in December; he faces a maximum of five years in prison.

The last key witness in the case, former mortgage broker Michael McGrath, is three years into a 14-year sentence for his role in a massive fraud scheme. McGrath, who testified that he helped funnel bribes from Fradella to Nagin, has not received a break on his sentence, but he may yet get one.

Follow Gordon Russell on Twitter, @gordonrussell1.