N.F.L. Commissioner Roger Goodell on Tuesday upheld his decision to suspend Jonathan Vilma, Will Smith, Anthony Hargrove and Scott Fujita for their reported roles in the New Orleans Saints’ bounty scheme.

The decision was expected; Goodell had imposed the original discipline. The players had called the league’s allegations that they were involved in a scheme that paid players for injuring opponents “specious,” claimed the N.F.L. had been on a “smear campaign” and dismissed the veracity of the league’s evidence. On June 18, Fujita emerged from an appeal hearing in front of Goodell and said, “I have yet to see anything that implicates me in some pay-to-injure scheme.”

Goodell wrote in a letter to the players Tuesday, “none of you has offered any evidence that would warrant reconsideration of your suspensions.” But he noted that if they presented such evidence, their suspensions could still be reduced. Vilma is suspended for the season, Hargrove for eight games, Smith for four and Fujita for three.