Updated: 8:55 p.m.
That could be Bengals wide receiver Chris Henry, but Goodell said he plans to meet with Henry before he makes a decision.
"There are a very few number of players. I think they are tainting the league," Goodell said. "I think they are tainting the other players. We need to get to it as quickly as possible and remove it. ... I probably have less understanding than most ... it's about protecting the shield. ... I assure you it will be stronger. ... We are expecting discipline will be stepped up."
Goodell said he plans to meet with Henry before rendering a decision on what many expect to be a multi-game suspension under the NFL's new get-tough policy for criminal behavior for his third and fourth arrests. Goodell indicated his call would come down before the April 28-29 draft.
"I'm hearing some prior to the draft and I'll have a decision prior to the draft on some cases," Goodell said when asked about lingering cases.
Marvin Frazier, one of Henry's agents, said Monday his client has a meeting next week with Goodell.
"He's doing what he has to do. He's out talking to kids, he's meeting with his probation officer, when the coaches want him to be at (the stadium), he's there," Frazier said. "These are things that happened a while ago and he's really trying to get his life together. Hopefully it's enough not to get a long suspension, but that's up to the commissioner and we'll see what happens after they meet."
Goodell said the new policy won't be retroactive, but he made it clear it will be tough: "The players that have had repeat offenses, we'll be dealing with them pretty harshly."
Goodell's revised policy will be discussed Tuesday with the coaches and owners and is expected to be adopted in the next few weeks. But he did say Monday that he's for fining and/or taking away draft picks from teams with repeat offenders. He indicated he would be going after teams that don't have "best practices" in place.
During the Bengals' spree of nine player arrests since January of 2006, Goodell offered more counseling to the Bengals and the club used some of them. When asked if he was satisfied with how the Bengals have responded to their players, Goodell said, "They've been very cooperative."
Goodell characterized "best practices" as educational and understanding of local laws and issues. The league also plans to expand the rookie symposium, which has dealt with the off-field transition for about a decade.
Goodell has been talking tough because he's got plenty of support from players, coaches, and club execs. When a guy like the esteemed Tony Dungy backs you no questions asked, it helps.
Dungy, head coach of the Super Bowl champion Colts, agrees with Bengals head coach Marvin Lewis and would like more say in discipline.
"I'd like to have more autonomy. There are times I wanted to do things and couldn't because it was collectively bargained or because it was league policy," Dungy said. "If you tell guys what you expect and what you want and you have the power to enforce it, you'll get what you want a lot of the time."
Goodell said the new policy is going to have guidelines, but he also said there won't be as anything as definitive as "three strikes and your out" for a year. But he also said he thinks he has the backing of people in the NFL that they don't have to wait for the judicial process to be resolved before dealing with repeat offenders. No one seems to mind right now that Goodell's discretion looks to be a bigger factor than any guideline.
"I'm fine with that if he makes it a tough policy," Dungy said. "Which I think he will."
Chiefs president Carl Peterson echoed the hallways buzzing with Goodell's commitment to conduct as one of his top priorities.
"It's clear the NFL is listening," Peterson said. "I'm looking for reasons (for the rise and scrutiny of criminal behavior). The media is so fast, so quick, it gets out there so quickly. There's no place to hide. You can't sweep it under the rug. The fans have a right to know when players are (misbehaving) on and off the field. Image is very important. It's essential to the continued success of the league."