NFL Commissioner Roger Goodell and players’ union chief DeMaurice Smith agreed to continue discussing changes to the league’s personal conduct policy following a four-hour session in New York on Tuesday.

In an email to player representatives afterward, Smith says he made it clear to the league that the union wants due process.

“While the league currently has great concern for its brand, fairness and justice for our members is more important,” Smith said.

“For us, the starting point for these discussions must be the desire to agree upon a fair personal conduct policy and domestic violence rules from a standpoint of prevention and education. We will not accept a world where all players are viewed as perpetrators first and husbands, fathers, sons and brothers second.”

Goodell and NFL officials were joined by Smith, the NFL Players Association’s executive director, Eric Winston, the union president, executive committee members Zak DeOssie and Jay Feely and other union staff.

“As the players and their union recognized in 2007 when the personal conduct policy was initially strengthened, misconduct by a few has a negative effect on everyone involved in the game,” NFL Executive Vice President Jeff Pash said in a statement.

“We look forward to full discussions with the NFLPA on these issues and to implementing a revised policy that upholds the standards that our fans expect and deserve.”

Smith says collective bargaining would provide the best outcome and points to the recent changes to the drug policy as an example.

“There, we achieved independent arbitration, and both sides were able to implement desired changes to the policies,” Smith said.

The NFL has been reluctant to bargain with the union over improvements to the personal conduct policy.

One potential hang-up: Goodell’s role in the disciplinary process.

The union favors a neutral arbiter in all such decisions, but the commissioner has been reluctant to cede power in those matters.

Troy Vincent, the NFL’s executive vice president of football operations, told The Associated Press in an email the discussion about a neutral arbiter “is on the table.”

Vincent also emphasized that the union was deeply involved in formulating the revised policy in 2007.

“We are trying to protect the players and remove conduct detrimental to the game,” Vincent wrote.

“Both the current and former players are part of the brand. When someone makes a mistake, we are all painted with the same brush.

“The league must take the highest road of service, and do what is right. This thought is not new: the game far exceeds one person. We believe we all share in the responsibility of preserving the game. There also must be personal accountability, which is not being discussed.

“We are not going to collectively bargain the game. What is bargained is hours, wages and working conditions. To that end, we are not going to sacrifice the game because it is too important to too many people. It is nothing new that employers have a right to establish the standards of employee conduct.”

Vincent, who played 15 seasons in the NFL, spent 13 years serving as a player advocate, union leader and president of the players association.

Goodell previously said he hoped a revamped personal conduct policy would be ready by the Super Bowl.