Goodell met Monday at NFL headquarters with New Orleans linebacker Jonathan Vilma, who is out for the 2012 season, and defensive end Will Smith, who has been docked for four games; Green Bay defensive end Anthony Hargrove, suspended for eight games; and Cleveland linebacker Scott Fujita (three games).
Vilma left first, after about an hour-long session in the morning.
The linebacker's attorney, Peter Ginsberg, said the NFL requested an adjournment to Monday afternoon, but he and Vilma refused. Ginsberg called the hearing "a sham" and said Goodell failed to present the evidence on which he based his decision to impose Vilma's penalty.
"Roger Goodell has taken three months to tear down what I built over eight years. It's tough to swallow. I have been linked to a bounty and it simply is not true," said Vilma, who is suing the commissioner for defamation.
"I don't know how I can get a fair process when he is the judge, jury and executioner. You're assuming it will be fair, but it's not."
Smith, Hargrove and Fujita had their appeals heard by Goodell at afternoon sessions, with their attorneys plus lawyers for the NFL Players Association on hand at the league's Manhattan offices.
Those players and Vilma all were on the Saints roster when then-defensive co-ordinator Gregg Williams, by his own admission, ran a pay-for-pain operation that handed out cash bonuses for big hits on targeted opponents.
The players dispute the league's contention that they were involved.
"The NFL's investigation has been highlighted by sensationalized headlines and unsubstantiated leaks to the media. I have yet to see anything that implicates me ... not in the last three months and not today," Fujita said. "The NFL has been careless and irresponsible, and at some time will have to provide answers."
The NFL's investigation of the Saints found Williams ran a system for three years under which payouts were set on specific opponents, including quarterbacks Brett Favre and Kurt Warner. The program was in effect from 2009, when New Orleans won the Super Bowl, through last season.
The league turned over some evidence to the four players and the union on Friday, as required by the collective bargaining agreement. That information included some 200 pages of documents, with emails, power-point presentations, even handwritten notes, plus one video recording.
After the hearings, the NFL showed reporters some of the material it used to confront players, including hand-written notes, documents from the Saints' computer system and witness testimony that showed an apparent bounty on Favre of $35,000 for the NFC championship against the Vikings in early 2010.
The initial complaint that sparked the investigation back in 2010 came from then-Minnesota coach Brad Childress, who heard of a price on Favre in the championship from a player.
Previously, Goodell suspended Saints coach Sean Payton for the season and assistant coach Joe Vitt for six games. Saints general manager Mickey Loomis got eight games, while Williams — now with the St. Louis Rams — was suspended indefinitely.
In a comment to investigators which the NFL shared Monday, Williams said: "We were rolling the dice with player safety and someone could've been maimed."Suggest a correction