The NFL players’ union wants the league and its owners to take disciplining players out of the hands of Commissioner Roger Goodell.

Already at odds over the process used to punish Ray Rice, the dispute heightened Tuesday when the league suspended Vikings running back Adrian Peterson for the rest of the season for using a wooden switch to discipline his 4-year-old son.

The central issue remains the same for both sides: Finding a way to fairly hold players accountable for transgressions that damage the credibility and image of the league and its players. The union wants disciplinary power now held by Goodell to be handled by a neutral arbitrator. The league, so far, doesn’t agree.

And while both the league and the NFL Players Association want to change the personal conduct policy, the sides disagree on how to do it. The union wants to bargain for changes to the policy, while the NFL wants to implement changes with union input the same way it changes rules on the field, like when it moved kickoffs to the 35-yard line.

Union chief DeMaurice Smith told The Associated Press in an email that the league indicated it was open to discussing the policy as recently as two months ago, but didn’t follow through in coming to the table. He said those discussions were distinct from the union representing Peterson in his case, though on a parallel track.

“There is one fact that does make those things similar though, and that is the NFL is clearly making things up as they go along,” Smith said Tuesday night. “Our goal is to pursue a new personal conduct policy that is fair, transparent and consistent. The only way that happens is if the NFL and the owners commit to collective bargaining.”

Troy Vincent, the NFL’s executive vice president of football operations, countered that Goodell’s authority was collectively bargained with the union in 2011, while the personal conduct policy in place nearly 20 years has never been part of contract negotiations.

“The union agreed to the Commissioner maintaining authority to discipline. The league believes it is in the best interest of football to retain that authority,” Vincent said. “The league is following the process dictated by the CBA.”

The union and players helped revise the personal conduct policy in 2007, Vincent said. He said the league has had multiple meetings with the union this year on revising the policy using the same approach.

The rules in place now have some players and agents wondering if the NFL has too much power and whether the union fell short by agreeing to give Goodell central power over discipline in 2011.

Agent Jerrold Colton, who represents four-time All-Pro tackle Jahri Evans of the Saints, Steelers cornerback William Gay and six-time Pro Bowl kicker David Akers, said the union’s failure to negotiate changes to the personal conduct policy in 2011 was a “tremendous oversight.”

“I felt strongly at the time that it was a mistake and clearly it’s turned out to be one for the players the way it’s played out and we’re stuck with it for another six years,” said Colton, who said he thinks the players and league absolutely need an independent, third-party arbitrator. “Due process exists in most places in the United States except in the NFL.”

Pittsburgh Steelers safety Mike Mitchell said the personal conduct policy needs more well-defined terms and clear guidelines based on precedent.

“Right now it’s kind of you know, one man has all the power and I don’t know if that’s ever really a good thing. I think Roger does his best to do the best that he can but I know he’s got a lot on his plate that he has to control,” Mitchell said. “I’m not just trying to bash him or come down on him but I think players would feel better if he wasn’t just judge, jury and executioner.”

Peterson pleaded no contest Nov. 4 to misdemeanor reckless assault in Texas for injuries to his 4-year-old son with a wooden switch. He said he intended no harm, only discipline.

Goodell told Peterson he will not be considered for reinstatement before April 15 for his violation of the personal conduct policy — the first example of a crackdown on players involved with domestic violence since stricter rules were put in place earlier this season.

The union, which announced it plans an appeal on behalf of Peterson, is demanding a neutral arbitrator oversee the hearing in the same way Rice’s case was handled. Rice is waiting for an arbirtrator to decide whether his indefinite suspension should be upheld or overturned. Goodell made Rice’s suspension more severe when video of Rice hitting his then-fiancee was released online.

Goodell has said he hopes to have a new personal conduct policy ready before the Super Bowl.

Vincent said the league’s internal process — including investigation, consulting independent experts, suspending players with pay and ultimately determining discipline — has been fair and transparent while following the collective bargaining agreement.

“In reality, those who are most upset with the personal conduct policy are those who violate it,” Vincent said. “The vast majority of players do not come into contact with the discipline process.”

Miami Dolphins defensive lineman Jared Odrick said he disagreed with Peterson’s punishment by the NFL, saying it showed how much scrutiny NFL players face over personal actions.

“It’s great and unfortunate that we’re at the forefront of America showing how to do good and bad. It’s a responsibility placed on us,” he said.

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AP Pro Football Writer Dave Campbell and AP Sports Writers Will Graves and Steven Wine contributed to this report.