(Reuters) - Suspensions for two players connected to the New Orleans Saints' bounty scandal were reduced by the National Football League (NFL) on Tuesday while two others, including Jonathan Vilma's season-long ban, were upheld.

Linebacker Scott Fujita's three-game ban was dropped to one game and free agent defensive end Anthony Hargrove's eight-game suspension was cut to seven games, the NFL said in a statement.

But Saints linebacker Vilma remained suspended for the entire 2012 NFL season while team mate Will Smith did not get his four-game ban reduced.

The four were punished in May when the NFL identified them as having leadership roles in a program where players were given cash rewards for knocking opponents out of games from 2009-2011.

But the bans were overturned by an arbitration panel ahead of the season-opening weekend last month in a decision that allowed NFL Commissioner Roger Goodell to put the suspensions back in place if he could prove there was an intent to injure.

Goodell decided to adjust certain aspects of the bans after recent meetings with each of the players, which marked the first time those players had agreed to speak directly to the NFL to give their side of the story, according 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," said Goodell.

"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."

Goodell said he could not determine that Fujita, who is now with the Cleveland Browns, directly contributed to the bounty pool but added that there was no question he was aware of it and its elements.

Hargrove will be credited for five games missed while a free agent, and will serve a two-game suspension once he is signed by a club, according to the NFL.

The NFL Players Association (NFLPA) said it will review the league's decision thoroughly and review all options.

"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 NFL Players Association said in a statement.

"The only evidence that exists is the league's gross violation of fair due process, transparency and impartiality during this process. Truth and fairness have been the casualties of the league's refusal to admit that it might have made a mistake."