Jonathan Vilma saw his suspension re-issued by the NFL on Tuesday. (Associated Press)

The NFL has re-issued the suspensions of four players in the New Orleans Saints bounty case, reducing two of the penalties.

NFL Commissioner Roger Goodell reduced the suspension of former Saints linebacker Scott Fujita, now with the Cleveland Browns, from three games to one, the league announced Tuesday.

The suspension of former Saints defensive lineman Anthony Hargrove, now a free agent, was reduced from eight games to seven. He will be credited with the five games he has missed as a free agent but must serve a two-game suspension when he is signed by a team, according to the league.

The four-game suspension of Saints defensive lineman Will Smith and season-long suspension of linebacker Jonathan Vilma were not changed. According to the league’s announcement, Vilma will retain the portion of the salary he received while on the physically unable to perform list for the season’s first five games.

An appeals panel overturned the original suspensions Sept. 7, two days before the Saints lost their season-opening game to the Washington Redskins at the Superdome.

At that time, the appeals panel said it was unclear whether the suspensions were imposed for conduct detrimental to the league, which is under Goodell’s jurisdiction, or for salary cap infractions, which are not. The panel sent the case back to Goodell and said he could re-issue discipline, if he chose to, after re-assessing the basis for the sanctions and making any necessary adjustments.

The players held a series of meetings with Goodell last month. The league said Tuesday that the suspensions are for conduct detrimental to the league.

“In my recent meetings with the players and their counsel, the players addressed the allegations and had an opportunity to tell their side of the story,” Goodell wrote in a memo to NFL teams, according to the league’s announcement. “In those meetings, the players confirmed many of the key facts disclosed in our investigation, most particularly that the program offered cash rewards for ‘cart-offs’.”

The players have denied the allegations and challenged the suspensions in federal court in Louisiana. They can appeal the suspensions re-issued Tuesday.

The NFL Players Association criticized Goodell’s decision in a written statement Tuesday.

“For more than six months, the NFL has ignored the facts, abused the process outlined in our collective bargaining agreement and failed to produce evidence that the players intended to injure anyone, ever,” the union wrote.

The ruling by the appeals panel had no effect on the suspensions of Saints General Manager Mickey Loomis, Coach Sean Payton, assistant coach Joe Vitt and former defensive coordinator Gregg Williams for their roles in the bounty scandal. Payton was suspended for a full season. Loomis was suspended for eight games, Vitt for six games and Williams indefinitely.

According to the league, Goodell wrote to Fujita that he did not conclude that the player contributed directly to the bounty pool, but “there is no serious question that you were aware of the pool and its elements.”

Goodell wrote to Hargrove that Hargrove misled a league investigator and obstructed the NFL’s investigation. He told Smith that he “endorsed and agreed to, and contributed substantial sums toward” the program. Goodell wrote to Vilma, according to the league, that Vilma offered “a substantial financial incentive to any member of the defensive unit who knocked Brett Favre out of the Saints’ 2009 NFC playoff game against the Vikings.”

The league’s investigation determined that amount to be $10,000.