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The investigation also found that Payton initially lied about the existence of a bounty program and instructed his defensive assistants to do the same.

Goodell showed a bit of leniency Monday, saying in a statement if Payton, Loomis and Vitt “embrace the opportunity and participate in a constructive way,” he would consider reducing the financial penalties on them. None of them has been fined, but each will lose significant amounts while not being paid their salaries during the suspensions. Payton, who twice apologized for his role in the bounties, could lose more than $6 million.

Goodell added he would consider modifying the forfeiture of the team’s 2013 second-round draft choice, perhaps to a lower round. But New Orleans still will receive a draft penalty next year and will lose this year’s second-round pick.

While the Saints await punishment for some players, they have the not-so-small task of finding an interim coach to replace Payton. They have talked to Bill Parcells, Payton’s mentor since their days together in Dallas, about coming out of retirement.

Parcells, who turns 71 in August, has said he would consider coaching the Saints if asked to help his former protege. Parcells won two Super Bowls with the New York Giants and took the New England Patriots to a Super Bowl, but has not coached since retiring from the Cowboys after the 2006 season, though he then worked in Miami’s front office.

If the Saints were to hire Parcells or anyone from outside the organization, the club would have to interview a minority candidate to comply with the NFL’s “Rooney Rule.”

Of course, the Saints could decide to promote from within the current staff, which has three strong candidates: offensive coordinator Pete Carmichael, defensive coordinator Steve Spagnuolo and offensive line coach Aaron Kromer.

Vitt also could be a candidate to step in, as he did briefly last season when Payton broke his leg, once his suspension ends.

Because Loomis can remain as GM until late summer, he will oversee the draft in late April and handle other roster moves. Loomis had been told by Saints owner Tom Benson to ensure that the bounty program was dismantled, but did not act.

Payton has said he laid out plans for the offseason training program and the late July beginning of training camp. The Saints play Arizona in the Hall of Fame game Aug. 5 in Canton, Ohio, the league’s first preseason game.

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AP Sports Writer Brett Martel in New Orleans contributed to this report.