Jones' career was revitalized in Cincinnati, where he signed in 2010 after injuries and legal issues during his time with the Titans and Cowboys besieged him in his first five years in the NFL.
Although he is 32, Jones has had some of his best individual performances in the past three seasons. Just before free agency started, Bengals defensive coordinator Paul Guenther said he felt Jones still had a lot of football left in him.
Jones sat out two full seasons, in 2007 because of a suspension and 2009, and that has started to benefit him late in his career. By not beating up his body for two seasons, Jones is still fresh enough at his age to be a valued contributor at cornerback.
Jones had 62 tackles and four interceptions last season. He was one shy of his career highs in both categories, despite missing two games with a nagging foot injury.
On the field, Jones still has some of that edge that most of his opponents dislike. Jones was fined $35,000 after last year's season opener when he ripped off rookie Amari Cooper's helmet and slammed his head on it during a scrum at the end of a play.
With seconds remaining in the Bengals' wild-card playoff game against the Steelers, Jones was flagged for making contact with an official as he tried to go after Steelers assistant Joey Porter, who had made his way onto the field.
After the game Jones also was critical of Steelers receiver Antonio Brown, claiming Brown faked a concussion that came on the same play Jones was penalized. Brown didn't play in Pittsburgh's divisional-round loss at Denver the next week.
Jones later publicly apologized to Brown. At the Super Bowl, Brown said he had not returned any of the private apologies Jones had left him.
Jones was flagged for his fewest penalties this past season since 2011.
ESPN Bengals reporter Coley Harvey contributed to this report.