CINCINNATI - Running back Rudi Johnson signed a one-year contract Tuesday with the Cincinnati Bengals, who already have a backup in place.

Johnson was a restricted free agent after last season, but the Bengals made sure he would stay by tendering a one-year, $1.8 million offer. No team was willing to match the offer and give the Bengals first- and third-round picks as compensation.

Johnson waited until after the Bengals' rookie minicamp to sign the one-year offer.

Top draft pick Chris Perry, a running back from Michigan, attended the minicamp over the weekend. The Bengals plan to use Perry to back up Johnson this season.