Saints veteran linebacker Scott Shanle tweeted that taking the whole season away from Vilma is "absolutely ludicrous!"
In a memo sent Wednesday to the NFL's 32 teams, Goodell reminded them that "any program of non-contract bonuses, however it is characterized, is a violation of league rules." Also, all players will be told how they can confidentially report rules violations.
In March, Goodell made Payton the first head coach suspended by the league for any reason, for trying to cover up the system of extra cash payouts. The Saints were fined $500,000 and lost two second-round draft picks.
Fujita, Hargrove and Smith are allowed to participate in offseason activity, including preseason games, before their suspensions take effect. Vilma, though, is suspended immediately and is not slated to be reinstated until after the next Super Bowl in February.
AP Football Writer Howard Fendrich and AP Sports Writers Rachel Cohen, Chris Jenkins, Tom Withers and Jon Krawczynski contributed to this report.
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.