One rule would ban peel-back blocks, and the other would keep teams from overloading one side of the defensive line on point-after and field-goal attempts.
The much-discussed crown-of-the-helmet rule proposal did not come up for a vote, according to the NFL Network. After a lively discussion of the controversial proposal, a vote was postponed until Wednesday.
Also, a vote on the infamous "tuck rule" is expected to come up with all indications that it would be eliminated.
The tuck rule allowed a fumbled ball moving forward in the hand of a quarterback to be called an incomplete pass.
The owners did pass a rule that the peel-back or chop block would be outlawed inside the tackle box. By the approved rule change, such a block would be a 15-yard penalty.
As for place kicks, the overload rule was created because kick defence teams were rushing through the gaps created by lining up more defensive players than the offence could block.
Defensive teams now can have just six or less players on each side of the snapper at the line of scrimmage. Players not on the line can't push teammates on the line into blockers, either.
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Denver Broncos executive vice president John Elway has said the team wants to re-sign free-agent defensive end Elvis Dumervil.
"We've offered Elvis a contract," Elway said. "We'd like to have Elvis back. We'd like to get it done as soon as possible, but I'm sure Elvis wants to see what else is out there."
The Broncos released Dumervil on Friday, about 35 minutes after he accepted a $4 million reduction in salary because the necessary paperwork wasn't filed by the deadline.
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Wes Welker's representatives have disagreed with New England Patriots owner Robert Kraft's version of the discussions that sent the popular receiver to the Denver Broncos.
The statement from Athletes First, released to NFL.com, said they received one "take it or leave it" offer that left no other choice except the free agency route, and that eventually led to the Broncos deal.
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Green Bay Packers president Mark Murphy has said the team is exploring a long-term contract with quarterback Aaron Rodgers.
Murphy told reporters at the owner's meetings that a deal would likely be done before the start of this season and make him the NFL's highest-paid player.
"It's a priority," Murphy said. "I think as an organization, I think we all want to see that get done."
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The Indianapolis Colts have agreed to a two-year deal with veteran quarterback Matt Hasselbeck, who was released by the division rival Tennessee Titans on Monday.
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As long as Tim Tebow remains property of the New York Jets, he'll get a chance to compete for the starting job, coach Rex Ryan said at the owner's meetings.
Ryan said embattled incumbent Mark Sanchez will begin the offseason program as the starter, but his spot isn't guaranteed.
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David Carr, who has attempted three passes the past two seasons with the New York Giants, has agreed to re-sign with the team as Eli Manning's seldom-used back-up. The Giants also announced the signing of receiver Louis Murphy.
Defensive tackle Randy Starks signed his franchise tender with the Miami Dolphins while Jacksonville centre Brad Meester has signed a one-year deal that will keep him with the Jaguars.
Offensive lineman Nate Garner re-signed with the Miami Dolphins, the Washington Redskins re-signed offensive tackle Tyler Polumbus and free agent cornerback D.J. Moore signed with the Carolina Panthers.
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The Dallas Cowboys and Miami Dolphins will play in the 2013 Hall of Fame game on August 4 in Canton, Ohio.
Bill Parcells, Larry Allen, Jonathan Ogden, Cris Carter and Warren Sapp will be inducted into the Hall of Fame in a ceremony August 3, along with two senior candidates, Curley Culp and Dave Robinson.