With the propriety of Tom Brady’s Deflategate suspension now set to be resolved in court and many of those in and around the sport expressing the view that the NFL’s system of justice is broken, the players’ union is vowing to address Commissioner Roger Goodell’s power to hear appeals in certain player-disciplinary cases in the next set of labor negotiations.

“It would be hard to imagine any new deal if there’s not a change,” Eric Winston, the veteran offensive lineman for the Cincinnati Bengals who is the president of the NFL Players Association, said in a telephone interview Tuesday. “I can’t imagine taking a new deal back to the players and say personal conduct isn’t going to change.”

Goodell rejected Brady’s appeal of the four-game suspension, which was imposed by the league under its integrity-of-the-game provisions. The NFL also cited Brady’s lack of cooperation with the league’s investigators. Goodell possesses similar powers to hear and resolve appeals of disciplinary measures taken against players under the personal conduct policy.

Winston expressed hope that the league and union might work out their differences on the subject before the expiration of the current collective bargaining agreement, which runs through 2020. But if that doesn’t happen, Winston said, the union will make neutral arbitration of disciplinary measures imposed by the league under the conduct policy a labor negotiating priority.

“We’re not against punishment where it’s deserved,” Winston said. “I’m not against setting boundaries. (But) there has to be a neutral arbitrator. You can’t tell me that keeping Roger Goodell in the position he’s in as arbitrator is going to win the confidence of the players. That’s long gone. You can’t go back and fix what’s happened.”

Winston and others on the players’ side of the sport said they believe the owners of the 32 NFL teams must step in and force changes to the league’s policies and approach on disciplinary matters. Peter Schaffer, an attorney and veteran agent, said the league’s approach to discipline is harming the image of players that the NFL should be promoting.

“I think the majority of the blame falls in the commissioner’s lap,” Schaffer said. “It comes from the fundamental flaw of a failure to believe the players are the greatest asset to the game. Punishing players publicly tarnishes the goodwill of the game. My son, outside of my house, appears to be the greatest child in the world. When I punish, I do it in-house.”

Not everyone agrees, particularly those on the management side of the sport. Owners John Mara of the New York Giants and Jerry Jones of the Dallas Cowboys expressed support for Goodell last week in the aftermath of New England Patriots owner Robert Kraft saying he was wrong to have trusted the league to handle DeflateGate and Brady’s suspension properly. Both the league and union filed federal lawsuits after Goodell’s rejection of Brady’s appeal.

“This is the system that the union helped to create in collective bargaining,” a high-ranking official with one NFL team said recently. “If they don’t like it, they should work to change it at the bargaining table instead of running to court every time there’s an outcome they don’t like.”

The collective bargaining agreement empowers Goodell to both impose discipline and to hear and resolve appeals in cases involving the integrity of the sport.

When the owners ratified the league’s revised personal conduct policy in December, the NFL put the power to make initial disciplinary rulings under the policy in the hands of a chief disciplinary officer. Goodell retained his power to hear and resolve appeals by players under the revised conduct policy.

The union said at the time that the league failed to collectively bargain the new policy with the NFLPA as required. It also said it would have been receptive to allowing Goodell to continue to make initial disciplinary rulings under the conduct policy if appeals are handled by a neutral arbitrator.

“They’ve pretty much refused to work with us on it,” Winston said. “They haven’t wanted to try to fix it. That’s what’s frustrating. We’ve made so many changes and fixed so many things. And when we’ve done things together, we’ve done pretty well.

“I don’t think you can look at anything we’ve done together and say it’s not working. When you don’t do it together, you don’t get the buy-in of the players and you get what you’re getting now. Unfortunately that’s the crazy area we’re in now. Instead of talking about the game, we’re talking about cases in federal court. That’s frustrating.”

The league has taken the approach that Goodell’s ability to resolve appeals in certain disciplinary cases is non-negotiable. Winston said the union plans to take an equally hard-line approach in the next CBA negotiations. He also said the union did not necessarily ignore the issue in the previous set of negotiations, which led to a 10-year labor deal being struck in 2011.

“I think it was a priority in the past,” Winston said. “It’s just hard to know when the other side is not going to live up to the deal. We never had these problems when Paul Tagliabue was commissioner.”

The sport’s use of neutral arbitration in cases under its drug policy and for cases involving illegal hits during games should be the model, according to Winston.

“I look at the other things we’ve fixed,” Winston said. “We fixed on-field fines. They can be appealed to a neutral arbitrator. Under the changes we made to the drug policy, there are appeals to a neutral arbitrator. I look at other sports, and it hardly gets any publicity because everyone knows the next step and knows the finality of it. . .. I just look at it and say, ‘How many of these do they have to get wrong before the owners ask what’s going on here?’ ”

The union applauded Goodell’s appointment of a former judge, Barbara Jones, to resolve Ray Rice’s indefinite suspension last year. Jones reinstated Rice.

The NFLPA opposed Goodell’s appointment of Harold Henderson, a former labor executive for the league, to hear the appeals of Adrian Peterson and Greg Hardy. Henderson upheld Peterson’s suspension but reduced Hardy’s suspension from 10 to four games.

The union took Peterson’s case to court and prevailed before U.S. District Judge David S. Doty, who sent the case back to the NFL for further proceedings under the CBA. Now the league and union are back in court over Brady’s case.

“The system is broken,” Schaffer said. “No offense to (Patriots backup quarterback) Jimmy Garoppolo, but the fans are not paying to see him. The fans and the people watching on TV are paying to watch Tom Brady and (suspended Cleveland Browns wide receiver)Josh Gordon. There are instances, like issues with domestic violence, where you have to do more than pay a fine and you have to suspend. But if you take, say, $4 million away from Tom Brady, that’s a hell of a punishment.”

Schaffer said the league suspends players too frequently, in his view, in non-violent cases.