Carpenter, the 18th pick of the 2006 draft for the Cowboys, never settled in at inside linebacker in the 3-4 scheme and seemed more suited to play the outside linebacker position in a 4-3 alignment.
"I think it's a great opportunity for me," Carpenter told ESPN 103.3 FM's Galloway and Company on Monday. "I get a chance to go to a 4-3. I'm getting a chance to start fresh, to start over and hopefully earn my way up here."
Carpenter's best game might have come in the 2006 playoff loss to the Seattle Seahawks in which he started and had five tackles -- including one for a loss -- and deflected three passes.
Carpenter was drafted by Bill Parcells, who coached Carpenter's father, Rob, a running back with the Giants from 1981 to '85. Carpenter became dispensable when the Cowboys moved up four spots in the second round of this year's draft and took Penn State linebacker Sean Lee with the 55th pick.
Lee is expected to fill Carpenter's role on special teams and as a backup linebacker.
"There's obviously a little disappointment leaving. We had a little unfinished business," Carpenter said. "We had four pretty good seasons while I was there. We never were able to kick the door in, get to the Super Bowl and possibly bring the Lombardi Trophy back to Dallas. I thought this season was a good opportunity to do that.
"Personally, this is going to be a tremendous opportunity, and I'm excited about it. I have a lot of football left in me, and I have a lot left to prove -- to myself and everybody else."
Like Carpenter, Barron has struggled. He never lived up to expectations in St. Louis despite starting in 74 of 76 career games since becoming a first-round pick in the 2005 draft.
"That experience is invaluable for a young offensive lineman," Cowboys owner and general manager Jerry Jones said in a statement. "It also speaks to his durability and versatility -- having started at both tackle positions. The process of managing an offensive line is always ongoing, and this acquisition was a great opportunity for our group."
Last year, he led the NFL with five holding calls.
Barron was benched for disciplinary reasons the second half of a loss to the 49ers last October.
"It's a different start," Barron told ESPNDallas.com on Monday after the trade was announced. "I get to see what the other side of the grass looks like."
The Cowboys last month released Flozell Adams, a five-time Pro Bowler, although fourth-year player Doug Free is expected to fill that opening. With the Cowboys, Barron will get the chance to challenge Free for the starting left tackle spot. If he doesn't win the job, he would become the swing backup tackle the Cowboys are seeking. Free was a fourth-round selection in 2007 and started the final seven games at right tackle for injured Marc Colombo, and stepped in for an injured Adams in the second half of the NFC divisional playoff game at Minnesota.
"A little competition, I'm up for that," Barron said.
Barron has signed his tender offer worth $2.73 million this season.
He joins a backup offensive line corps that also includes Travis Bright (center/guard), Montrae Holland (guard), Robert Brewster (left tackle), Pat McQuistan (guard), Cory Procter (center/guard) and rookie Sam Young (right tackle).
The trade is the Cowboys' biggest offseason move since they released a pair of veterans in Adams and free safety Ken Hamlin. The Cowboys have elected to move Free and Alan Ball into their starting positions.
Dallas also re-signed its only unrestricted free agent in Holland.
Next on the Cowboys' agenda is to extend the contracts of two of their restricted free agents: wide receiver Miles Austin and strong safety Gerald Sensabaugh. Jones said he would like to sign both to long-term deals.