Williams' agent, Leigh Steinberg, wrote in an e-mail to The Miami Herald that Williams received a letter from the Dolphins dated Dec. 31 and signed by Parcells renewing Williams' contract for 2008.

Steinberg wrote that he will wait until Parcells has a chance to settle in with the Dolphins before contacting him. Steinberg also wrote that Williams is doing well in his rehabilitation from a torn pectoral muscle that ended his 2007 season after six carries against the Pittsburgh Steelers on Nov. 26.

Such a letter would seem to indicate that Parcells wants Williams back next season. That is not surprising from a practical perspective. There is no certainty how soon — or if — Ronnie Brown will recover from a torn knee ligament that ended his season as he was piling up 100-yard rushing games at 5.0 yards a carry. Even if Brown recovers fully, having a healthy Williams would give the Dolphins the kind of two-back tandem that is popular in the NFL.

Also, if Williams can shake off the rust of being a 31-year-old who has played 12-plus games in the past four seasons, it would give the Dolphins another asset they could trade. New Dolphins general manager Jeff Ireland doesn't have a track record as far as trade tendencies, but his direct boss is well-known for being willing to deal, and he might encourage Ireland in that direction.

Williams is set to make $730,000 next season, hardly expensive for a running back playing well.

Twice recently, Parcells made statements that seemed to preclude Williams rejoining the Dolphins.

At his introductory media session last Thursday, Parcells said: "I'm interested in good-character people. I don't want thugs and hoodlums on the team. I really don't. I don't want bad-character guys. I don't want problem children. I'm more willing to let someone else try to address those things with other people."

On Monday, Parcells spoke to the Virginia Tech team, in town for the Orange Bowl: "I'm not looking for any dope heads, lazy guys. I'm looking for football players."

There's no record of anyone who has met Williams accusing him of being a thug or a hoodlum. In fact, he is shy and polite, and many people from across a massive economic and ethnic range find him an interesting conversationalist — particularly if the topic isn't football. Teammates have all but sung praises to Williams' work ethic. Brown has credited Williams' diligent example in 2005 for helping him understand what it took to be a professional.

Williams' substance-abuse issues with marijuana — multiple failed drug tests leading to his 2004 "retirement" and his suspension for the 2006 season — would seem to throw him into the "problem child" category.