The Bengals waived kicker Dave Rayner, who had a head start in the competition after Nugent was hurt. Nugent finished strong, going 3 of 4 on field-goal attempts, including two from beyond 50 yards.
Jones was Jacksonville's first-round draft pick in 2005. He was arrested and charged with cocaine possession in 2008, drawing a three-game suspension from the NFL. The Jaguars waived him after he was jailed for violating his plea agreement.
Jones caught just four passes for Cincinnati during the preseason.
As expected, cornerback Adam "Pacman" Jones made the team as a third cornerback and punt returner. Jones also is trying to revive his career after spending last season out of football.
The Bengals made 22 moves to reach the 53-man roster limit Saturday. The defending AFC North champions open the season Sept. 12 at New England.
Two 2010 draft picks were waived: fifth-round guard Otis Hudson and sixth-round wide receiver Dezmon Briscoe.
Copyright 2010 by The Associated Press