Bill Parcells has one haunting memory from a coaching career that will culminate with his Aug.3 induction into the Pro Football Hall of Fame: his bitter post-Super Bowl XXXI divorce from the New England Patriots and owner Robert Kraft after the 1996 season.

"I regret leaving New England. Had we done things differently ... " Parcells recently told USA TODAY Sports. "I had a good young team there. I hated to leave that team, because I knew what we could do.

"I was absolutely too headstrong. And he might have been a little headstrong, too. I think both Kraft and myself, retrospectively, would have done things a little differently."

And the course of NFL history would have changed.

Parcells was succeeded in New England in 1997 by Pete Carroll, who coached the Patriots for three seasons before he was replaced by Bill Belichick in 2000.

The Patriots have won three Super Bowls and reached two others under Belichick, who, without the New England job available, might have remained head coach of the New York Jets for more than a day before resigning to move up the road to Foxborough, Mass.

Parcells and Kraft have made their peace, getting over a breakup caused by Parcells' lack of final say on building the roster, which was decided by then-director of player personnel Bobby Grier. That power struggle led Parcells to taunt Kraft with the famous line: "If they want you to cook the dinner, at least they ought to let you shop for some of the groceries."

Kraft recalled the truce, which happened about 10 years ago.

"At a Super Bowl, Bill was standing there as I approached, and he just said to me, 'If I had to do it all over again. I would have done things differently.' And I said, 'So would I,'" Kraft told USA TODAY Sports.

"It would have been pretty special," Kraft said. "We were just coming at it from different times. And so much in life is timing. But in the end, we have a great relationship today. I have great respect for him. He did a great deal for our franchise. And I will forever be grateful for that."

Parcells didn't fly home with the Patriots from New Orleans after the Super Bowl loss to the Green Bay Packers, and he abruptly left for an advisory job with the Jets that soon became the head coaching gig.