An NFL arbitrator ruled Monday that he does not have the authority to discipline three of the four players suspended by the league in the New Orleans Saints bounty case.

Stephen Burbank, the sport’s system arbitrator, ruled that he does not have jurisdiction over the penalties given to linebacker Jonathan Vilma, defensive end Will Smith and linebacker Scott Fujita, who now plays for Cleveland. Burbank was responding to a grievance filed by the NFL Players Association, which announced it would appeal his decision.

Burbank ruled that he may have jurisdiction over the discipline imposed on Anthony Hargrove, now a defensive end for the Green Bay Packers, pending clarification by the NFL of the conduct that led to Hargrove’s suspension.