League commissioner Roger Goodell on Tuesday reduced Anthony Hargrove's ban from eight games to seven and Scott Fujita's suspension from three games to one, but upheld the year-long suspension of Jonathan Vilma and the four-game suspension of Will Smith.
The league will now schedule hearings on the appeals, NFL spokesman Greg Aiello said.
All four players have asked that Goodell recuse himself from the appeals process, sources said.
The players are eligible to be paid during the process and no suspensions will take effect until the appeals process is completed, Aiello said.
Fujita now plays with the Cleveland Browns while Hargrove is a free agent. Vilma and Smith remain with the Saints although the injured Vilma is unable to play.
The players originally were suspended in May for their roles in what the NFL called a bounty scandal by the Saints that ran from 2009-11 with players being paid to injure opponents.
But the bans were overturned by an arbitration panel ahead of the season-opening weekend in a decision that allowed 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 meetings with each of the players.
