updated 8:31 p.m. ET Sept. 3, 2006

When Bill Belichick is asked to identify the coaches who influenced him, he begins with Ted Marchibroda and tacks on a list of relative unknowns, including, of course, his father Steve, a career assistant at Navy who died last November.

The name Parcells is never uttered, at least not this century. For Belichick and Bill Parcells, who spawned one of the NFL’s most successful coaching trees, have been on very different wavelengths since Belichick split from the Jets and his one-time mentor in 2000.

But the ice has melted a bit lately. The two most successful members of the Tuna Tree, who barely acknowledged each other for six years, are now a little chummier, chatting from time to time this summer in a limited way about workings of the 3-4 defense and how to run a practice.

“I don’t want to tell you this was a lengthy conversation,” Parcells said this week. “But I have talked to him say 4-5 times in the last month. He’s a guy I think a lot of. He knows what my problems are. It’s a good sounding board, that’s all. I’m probably using him right now more than he’s using me.”

That might help Parcells. Belichick’s Patriots have won three Super Bowls in the last five years and the Tuna, now in Dallas, hasn’t won a title — with three different teams — since he got his second ring after the 1990 season with the Giants.

That date is significant, because that team from the Meadowlands spawned one of the most successful coaching trees in the NFL and the upper echelons of college football.

It goes back to 1975, when Parcells hooked up with another young assistant at Texas Tech named Romeo Crennel. But it flows from that 1990 team that beat Buffalo 20-19 in the Super Bowl remembered most for Scott Norwood’s missed field goal in the final seconds.

Crennel, now trying to rebuild a Cleveland franchise that was reborn into chaos in 1999, is one of seven head coaches from that staff.

Roll call: Parcells, Belichick, Tom Coughlin (85-75 lifetime with the Jaguars and Giants), Crennel, Al Groh (Jets and Virginia), Charlie Weis (Notre Dame) and Ray Handley (Giants 1991-92). Plus Ron Ehrhardt, who coached the Patriots from 1979-81 — his 1980 staff included a young linebackers coach who in that year was given the nickname “Tuna” by his players.

Handley is the only clunker in there, going 14-18 in two seasons with a team that included Lawrence Taylor, Phil Simms and a bunch of other veterans from that second Super Bowl winner. For one year, Maurice Carthon, now Crennel’s offensive coordinator in Cleveland, was a running back under Handley. Pepper Johnson, now Belichick’s defensive line coach in New England, played linebacker in New York back then.

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Two more eventual head coaches, perhaps.

There are, of course, other great coaching trees, notably the one that traces back to Bill Walsh, architect and coach of the San Francisco 49ers who, with Parcells’ Giants and Joe Gibbs’ Redskins, dominated the NFC — and the NFL — during the 1980s.

Walsh turned over the 49ers to George Seifert in 1989, and Seifert won two Super Bowls.

But the bigger group of graduates was spawned through Mike Holmgren, the offensive coordinator on the later Walsh teams. Holmgren’s Green Bay staff included future head coaches Ray Rhodes (who began with Walsh), Jon Gruden, Andy Reid, Mike Sherman and Marty Mornhinweg (the Ray Handley of that group.)

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There also is a historic link: Paul Brown, the father of all modern coaches, whose pro career began with the Cleveland Browns in 1946.

Walsh worked for Brown in Cincinnati, and even Parcells has ties to Brown through George Young, who gave him his first NFL head coaching job with the Giants in 1983.

Young’s first job in football was with Don Shula, first in Baltimore and then in Miami until he got the GM’s job in New York in 1979. Shula has always credited his coaching career to Brown, who also ran the Cincinnati Bengals almost until his death in 1991.

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But the Tuna Tree is unique in a number of ways beyond its on-field success.

For one thing, its members set similar rules, such as putting assistants off limits to the media much of the time. Weis, notably, often sounds like Parcells, often adding “OK” to emphasize a point.

“Several people say it and especially my wife,” Weis said after he was hired by Notre Dame. “It’s not exactly the same but, really, I’m from Jersey, he’s from Jersey. ... He’s earned the right to bust chops with the media. So I have to pick and choose my spots and be more tactful, because people are like, ’What have you ever done?”’

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