NEW ORLEANS — NFL commissioner Roger Goodell upheld the suspensions of Jonathan Vilma and Will Smith Tuesday for their role in the Saints bounty scandal and reduced penalties for Scott Fujita and Anthony Hargrove.

Vilma will sit out the entire season and Smith’s punishment stands at four games.

Hargrove, a free agent defensive lineman, will face a two-game suspension once he signs with a team. He originally was hit with eight games, but that was reduced to seven with five games already served. Fujita, who plays for Cleveland, will now miss only one game instead of three.

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The players were implicated in what the NFL said was a bounty pool run by former Saints defensive coordinator Gregg Williams and paid improper cash bonuses for hits that injured opponents. The players have acknowledged a pool but denied they intended to injure anyone.

Goodell’s new ruling comes about a month after an appeal panel created by the NFL’s labor agreement vacated the original suspensions on technical grounds and informed Goodell that he needed to clarify the reasons for the punishment.

Only Smith and Fujita have played this season. Vilma has been recovering from offseason knee surgery and hopes to return in two weeks when the Saints play at Tampa Bay.

The players can further delay their suspensions by appealing again through their labor contract. They could also ask a federal judge in New Orleans to revisit their earlier request for an injunction blocking the suspensions.

‘‘The quality, specificity and scope of the evidence supporting the findings of conduct detrimental are far greater and more extensive than ordinarily available in such cases,’’ Goodell said in a memorandum to the 32 clubs.

‘‘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 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,’ that players were encouraged to ‘crank up the John Deere tractor’ and have their opponents carted off the field, and that rewards were offered and paid for plays that resulted in opposing players having to leave the field of play.’’

The NFLPA remained critical of Goodell’s decision to punish the players and the process by which he reached his decisions.

‘‘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,’’ they said in a written statement. ‘‘The only evidence that exists is the League’s gross violation of fair due process.’’

Goodell began to reconsider his disciplinary actions after the Sept. 7 appeal panel ruling and this time all four players agreed to meet with him. During those meetings the NFL produced sworn declarations by Williams and another former defensive assistant, Mike Cerullo, in which they stated that they observed Vilma offering what they believed were $10,000 rewards for knocking then-Arizona quarterback Kurt Warner and then-Minnesota quarterback Brett Favre out of 2009-10 playoff games.