The NFL is considering toughening its penalties for players who commit acts of domestic violence, including a potential one-year ban for a second offense, according to multiple people familiar with the league’s recent deliberations.

The prospective new policy, if it is implemented, could establish guidelines for a suspension of four to six games without pay for a first offense and potentially a season-long suspension for a second incident, according to those with knowledge of the matter. They spoke on the condition of anonymity due to the sensitivity of the topic and because no final decision has been made by the league on implementing the policy.

The contemplated changes, if they are made by the NFL, would come after the league and Commissioner Roger Goodell have been criticized heavily for the two-game suspension imposed on Baltimore Ravens running back Ray Rice for allegedly striking Janay Palmer, the woman who is now his wife. Many media members and other observers have called Rice’s suspension insufficient and said it sends the wrong message about the league’s attitude toward domestic violence.

It was not clear if the potential new policy faces any significant obstacles to being put into effect.

“We need to have stricter penalties,” said one person with knowledge of the league’s deliberations on the matter. “I think you will see that. I believe the commissioner and others would like to see stricter penalties. We need to be more vigilant.”

That person said Goodell and the league “tried to stick with precedent” from previous NFL disciplinary measures when deciding on the length of Rice’s suspension.

“A lot of us were disturbed by what we saw” in the Rice case, the person said. “I think you will see something in probably the next few weeks. A first offense could be four to six games, definitely more than two. A second offense might be a year.”

A second person who had been briefed on the matter confirmed that the increased penalties are under consideration. That person said he did not know if it is definite that the new policy will be enacted nor when the new policy, if implemented, might go into effect.

The NFL declined to comment through a spokesman.

Two people with close ties to the NFL Players Association said the union was not involved in the deliberations.

Rice’s suspension resulted from an incident in February in which he allegedly struck Palmer, then his fiancée, in a hotel elevator in Atlantic City. Video became public showing Rice pulling an apparently unconscious Palmer from the elevator. The couple later married. Rice pleaded not guilty to a third-degree aggravated assault charge and avoided trial when he was accepted into a pretrial intervention program.

Rice was suspended from the Ravens’ first two games of the upcoming season without pay and was fined an additional game check based on last season’s salary. He will lose about $529,000 from the NFL’s penalty.

Goodell has defended the length of the suspension. When he spoke to reporters while in Canton, Ohio, for the Pro Football Hall of Fame induction ceremonies, he said that the punishment “has to be consistent with other cases, and it was in this matter.”