A former federal prosecutor who assisted the league in its investigation of the New Orleans Saints’ bounty program said Thursday that NFL Commissioner Roger Goodell had sufficient evidence to impose the suspensions announced this week.

“It is a rare situation where you have multiple independent sources with first-hand knowledge,” Mary Jo White, a New York-based attorney who formerly was the U.S. attorney for the Southern District of New York, said in a conference call with reporters. “This is not something based on what somebody else said to them. It is an unusually strong record on which the commissioner acted.”

The league announced Wednesday that Goodell had suspended four players for their roles in the bounty scandal. The league concluded that players received cash bonuses for hits that injured opponents.

Saints linebacker Jonathan Vilma was suspended for the entire season without pay. Saints defensive end Will Smith was suspended for four games, defensive lineman Anthony Hargrove, now with Green Bay, was suspended for eight games, and linebacker Scott Fujita, now with Cleveland, was suspended for three games.

Vilma and Smith denied the allegations against them in written statements Wednesday. The NFL Players Association announced that it had not received specific or detailed evidence of a pay-to-injure scheme.

But White said Thursday: “The evidence overwhelmingly supported the charges.” She said she reviewed the evidence and the NFL’s investigative process for the league at its request. She said she has represented the NFL in a variety of legal matters since returning to private practice in 2002.