Parcells was 34-32 in Dallas, counting two playoff losses. He had one year left at more than $5 million on a contract extension signed last January.

“He’s meant so much to, not only the Cowboys and Giants and Patriots and Jets, teams that he coached, but for the NFL in general,” Bears coach Lovie Smith said. “His teams have always played at a certain level so we’re losing one of our all-time great coaches. For him, though, I think it’s always good when you see a football coach that decides that he’s had enough, a guy that goes out on his own terms, and guys like Bill Parcells should get an opportunity to do that.”

Parcells isn’t exactly rushing out the door.

“Bill will continue to come to work here at Valley Ranch throughout at least the end of this week, and we will continue to meet and address the present status of our team while also discussing the future,” Jones said. “Clearly, we wanted Bill to return for next season, but I am completely understanding and respectful of his decision to retire from coaching.”

A team spokesman said Jones and Parcells will discuss various aspects of the organization — though not necessarily the person Parcells thinks should take his place.

Parcells spent 15 days since the Seattle game deciding what to do. During that time, four other teams picked new coaches and a fifth, Oakland, ended its search Monday night.

Jones has given no indication of what kind of coach he’d hire next. In his statement, there was only one hint: “Bill’s coaching the Cowboys represented a willingness to embrace a different philosophy and approach toward winning. This experience will reinforce that willingness to be flexible.”

Jones could go for proven a commodity such as Bill Cowher, recently resigned from Pittsburgh, but he would require compensation to the Steelers and a massive salary. He also might chase a big-name college coach, from Notre Dame’s Charlie Weis, Oklahoma’s Bob Stoops to Southern California’s Pete Carroll, who replaced Parcells in New England a decade ago.

Slideshow   The Week in Sports Pictures A kayaker flips out, a racehorse eyes the Triple Crown and more. more photos

Or, maybe Jones will pursue Chicago defensive coordinator Ron Rivera, or former NFL coaches like San Diego defensive coordinator Wade Phillips or San Francisco offensive coordinator Norv Turner. Turner would be a popular choice locally; he called plays for Dallas’ Super Bowl team in 1992 and remains close to Troy Aikman.

The next coach will have to deal with Jones as general manager. And he’ll face a decision of what to do about receiver Terrell Owens, who is due a roster bonus in March.

T.O. certainly isn’t the Big Tuna’s problem any more.

Parcells has retired and insisted he’s done for good only to return several times before. However, this time, he’s older, was well-paid by Jones and has a new home in Saratoga, N.Y.

Even if this really is it, his influence on the game will remain because of all the coaches who worked for him, from three-time Super Bowl champion Bill Belichick of New England to New Orleans’ Sean Payton, this past season’s coach of the year. Tom Coughlin of the Giants and Romeo Crennel of Cleveland also paid their dues under Parcells.

“We’re going to miss Bill Parcells on the sideline and we’ll miss him in the NFC East,” Coughlin said. “I think Bill’s looking forward to having the opportunity to do some of the things he truly wants to do. I wish him well.”