CINCINNATI — Tank Johnson, a player with legal troubles in his background, is joining the Cincinnati Bengals, a team that frequently has dealt with such issues.

The defensive tackle agreed to a contract with the Bengals on Tuesday. His agent, Jerrold Colton, says the Bengals’ defensive scheme is a better fit for Johnson than his previous team, the Dallas Cowboys.

The 27-year-old free agent had 33 tackles and three sacks in two seasons with the Cowboys, who signed him even while Johnson was still serving an eight-game NFL suspension in 2007 for violating the league’s conduct policy.

Johnson was released by the Bears in June 2007, days after he was pulled over by police in Gilbert, Ariz., for speeding. There were never any charges in the Arizona case, but Johnson had already served a two-month jail term for violating probation from an earlier gun charge when he had unregistered firearms in his home.

While with the Bears, he helped them win the 2006 NFC title before they lost to Indianapolis in the Super Bowl.

Johnson had no off-field problems with Dallas.

The Bengals have a history of giving second chances — and third and fourth chances — to players who get into trouble. Linebacker Odell Thurman and receiver Chris Henry were the most high-profile examples, piling up the arrests and suspensions.

In all, the Bengals had a run of 10 player arrests in a 14-month span.