Neither move was a surprise. Dockery had become a bench-sitter who was due $3.8 million in salary in 2011, and Carter was a poor fit for the team's 3-4 defense.
NFL Network insider Jason La Canfora cited league sources in reporting that the Redskins also plan to cut veteran defensive tackle Ma'ake Kemoeatu by Thursday. Kemoeatu had 29 tackles in 14 games last season, but he missed the last two contests because of a left shoulder injury.
Dockery hadn't missed a game in his eight-year NFL career, playing in 116 consecutive in the regular season, before he was made inactive in Week 5. Dockery, whose starting job was taken by Kory Lichtensteiger, played in only one more game the rest of the season.
"I know I can play in any scheme, man," Dockery said. "All is well, though. I'm looking ahead to what's next. I'm approaching this offseason and making sure that I'm in the best shape I've ever been. I feel good, I'm healthy, and I know I still have great ball let in me."
The moves came one day after the Redskins released running back Clinton Portis rather than pay him $8.3 million next season. It wasn't that long ago that Portis, Dockery and Carter were premium-paid, reliable members of the starting lineup, but all will be at least 30 by the start of the next season and have no place in Shanahan's plans.
Dockery shared fond memories about his time with the Redskins, including springing a block for Portis during the 2005 playoffs.
"The Redskins will always hold a special place in my heart," Dockery told The Post. "I had a chance to play for some unbelievable coaches in Joe Gibbs and 'Buges' (offensive line coach Joe Bugel). The fans here have always been tremendous. Even when I went (to Buffalo) and would come back, they showed me love. I'm going to retire here. This will be my home."
Dockery was drafted by the Redskins in the third round in 2003 and hit the free-agent jackpot twice in a short amount of time. He left Washington in 2007 to sign a seven-year, $49 million deal with Buffalo, but the Bills cut him after two seasons. He then returned to the Redskins to sign a five-year, $26.5 million contract with $8.2 million guaranteed in 2009.
Carter had 11 sacks in 2009 while playing defensive end in a 4-3 scheme, but he struggled when moved to linebacker last season in the 3-4. He started in just five games and had 2.5 sacks, symbolic of the argument that the Redskins switched their defensive scheme before they had the personnel to make it work.
The Redskins also made a second-round tender offer to restricted free-agent linebacker Chris Wilson. The tender is subject to whatever free-agent rules are included when the NFL and the players' union reach a new collective bargaining agreement after the old one expires Thursday night.
The Associated Press contributed to this report.