By BRETT MARTEL, AP Sports Writer

NEW ORLEANS (AP) — Former NFL Commissioner Paul Tagliabue has advised league officials and players implicated in the NFL's bounty probe that he plans to complete all hearings by Dec. 4 and make a ruling shortly after.

In a document obtained Wednesday by The Associated Press, Tagliabue directs the NFL to produce key witnesses in the Saints cash-for-hits program, including former defensive coordinator Gregg Williams and former defensive assistant Mike Cerullo.

Four players initially were suspended, but those punishments were vacated and Tagliabue was selected to oversee new hearings. Meanwhile, Saints LB Jon Vilma and DE Will Smith are still playing.

Even as Tagliabue moves the process forward, a federal judge is still considering arguments by players that Tagliabue should be removed as arbitrator because he is biased in favor of the NFL. Based on the schedule laid out by Tagliabue, U.S. District Judge Ginger Berrigan could choose to rule as early as next week.

For now, only Williams, Cerullo, Vilma, Saints assistant head coach Joe Vitt, NFL chief security officer Jeff Miller are the only scheduled witnesses.

They are scheduled to appear in a series of hearings in Washington D.C. running from Tuesday through Dec. 4. That means Vilma and Smith likely will be available at least for the Saints' next two games against San Francisco this Sunday and at Atlanta on Nov. 29. They could also play at the New York Giants on Dec. 9.

None of the players have served a single game of their suspensions yet, though Vilma was barred from attending Saints training camp before commissioner Roger Goodell's initial rulings were vacated during Week One of the regular season.

Vilma initially was suspended the entire 2012 season and Smith for four games.