A couple of accomplished NFL pass rushers suddenly became available when Julius Peppers and DeMarcus Ware were released to create room under the salary cap in two of the biggest moves at Tuesday’s start of the free-agency signing period.

The Bears cut ties with Peppers, who has 118½ sacks in 12 seasons, as part of a series of moves aimed at improving their defense, including agreeing to a five-year contract with former Raiders end Lamarr Houston.

The Cowboys let Ware and his 117 sacks go.

“A decision like this, involving a man who is a cornerstone player in the history of your franchise, is extremely difficult,” Dallas owner Jerry Jones said. “We were also in very strong agreement that playing for the Dallas Cowboys would be one of the options we would both be exploring.”

With the cap rising $10 million to a record $133 million, a crop of players quickly found new homes as soon as the market officially opened Tuesday afternoon – and defensive backs and offensive linemen were a popular commodity.

About 5½ hours after free agency began, one of the top players available, three-time Pro Bowl safety Jairus Byrd, agreed to terms with the Saints, part of a merry-go-round of moves at his position. Other safeties swapping clubs: Michael Jenkins, from the Saints to the Eagles; Donte Whitner from the 49ers to the Browns; Antoine Bethea from the Colts to the 49ers; Aqib Talib from the Patriots and T.J. Ward from the Browns to the Broncos; Mike Mitchell from the Panthers to the Steelers; Ryan Mundy from the Giants to the Bears; and Alterraun Verner from the Titans to the Buccaneers.

In addition to jettisoning Peppers and adding Houston and Mundy, Chicago agreed to one-year deals with linebackers Jordan Senn and D.J. Williams.

Deals for offensive linemen were highlighted by Pro Bowl left tackle Branden Albert’s five-year contract with the Dolphins. Albert left Kansas City to take over the position played at the start of last season by Jonathan Martin, whose exit from Miami in October led to an NFL inquiry into bullying on the team.

Late on Tuesday, Martin was traded by the Dolphins to the 49ers.

Left tackle Jared Veldheer and the Cardinals agreed to a five-year contract worth up to $35 million. Veldheer left the Raiders, who replaced him by giving former Rams lineman Rodger Saffold a five-year deal. Another left tackle, Eugene Monroe, agreed to a five-year contract to stay with the Ravens.

Guards switching teams: Zane Beadles was joining the Jaguars from the Broncos, pending a physical; the Falcons agreed to terms with Jon Asamoah, who left the Chiefs; the Redskins struck a deal with Shawn Lauvao, who left the Browns. The Redskins also agreed to terms with Cardinals special teams standout Adam Hayward and receiver Andre Roberts and scheduled a visit with cornerback Corey Graham.

The Jaguars also were busy, re-signing cornerback Will Blackmon to a two-year deal, a trade that sent quarterback Blaine Gabbert to the 49ers for a sixth-round draft pick and an agreement with former Vikings running back Toby Gerhart.

Other players changing teams: kick returner and receiver Dexter McCluster went to the Titans from the Chiefs; defensive end Arthur Jones joined the Colts from the Ravens; defensive end Tyson Jackson and defensive tackle Paul Soliai joined the Falcons; and defensive tackle Earl Mitchell left the Texans for the Dolphins.

Amid it all, the Peppers and Ware departures were the most significant developments.

The 31-year-old Ware, who went to seven Pro Bowls while in Dallas, was set to count $16 million against the salary cap. By releasing him now, the Cowboys, who were right up against the cap, saved more than $7 million. Ware had a career-low six sacks last season, his ninth in Dallas. He missed time with a thigh injury, then had offseason elbow surgery.

Others released included Eagles safety Patrick Chung, Bengals center Kyle Cook, Falcons safety Thomas DeCoud, Bills quarterback Kevin Kolb (who failed a physical), 49ers cornerback Carlos Rogers and Steelers linebacker LaMarr Woodley.

Among players staying put:

DT Jonathan Babineaux got a three-year contract from the Falcons.

RB Joique Bell now is signed with the Lions for $9.3 million over three years, with $4.3 million guaranteed.

WR Andre Caldwell got a two-year contract from the Broncos.

CB Vontae Davis re-signed with the Colts.

TE Anthony McCoy got a one-year deal from the Super Bowl champion Seahawks after he missed all of last season with a torn Achilles tendon.

RB Darren McFadden was given a $4-million, one-year contract by the Raiders.

WR Santana Moss and LB Perry Riley re-signed with the Redskins.

KR-WR Brandon Tate re-signed with the Bengals.

PK Adam Vinatieri, the 41-year-old with four Super Bowl rings, agreed to a two-year contract with the Colts.

Other PKs getting new contracts: Dan Carpenter (Bills), Phil Dawson (49ers) and Nick Folk (Jets).

AP Sports Writers Bob Baum, Tim Booth, Schuyler Dixon, Josh Dubow, Larry Lage, Mark Long, Michael Marot, Janie McCauley, Paul Newberry, Teresa M. Walker, Dennis Waszak Jr., John Wawrow, Joseph White and Steven Wine contributed to this report.