The Redskins have to decide whether they can afford to bring back safety LaRon Landry, right. The team has been docked $36 million in salary cap space over the next two seasons, and already cut last year’s other top safety, Oshimogho Atogwe. (John McDonnell/The Washington Post)

With their first two picks in the 2012 NFL draft spent after Friday’s blockbuster trade to the St. Louis Rams, the Washington Redskins — who previously figured to be active in the free agent market — are likely to step up their efforts to add the players crucial to improving this season.

The addition of an elite rookie quarterback — most likely Baylor’s Heisman trophy winner, Robert Griffin III — and $40 million to spend under the NFL’s $120.6 million salary cap should help their chances of landing a top wide receiver, a right tackle, a left guard and perhaps a cornerback and a safety when free agency opens at 4 p.m. on Tuesday.

“We thought it was important to do [the trade with St. Louis] before free agency to allow us the proper planning, and to know what you’re going to get with your first pick in the draft,” said Redskins General Manager Bruce Allen. “It gives you great comfort and allows us to execute the game plan that we developed in early January.

But the NFL may have complicated those efforts Monday when it took $36 million in salary cap space away from the Redskins, a penalty assessed because of the way the Redskins structured player contracts in 2010, when the league had no salary cap, according to people familiar with the matter. The league is taking similar action against the Dallas Cowboys, who will lose $10 million, according to one of those people.

The teams can decide how to distribute the cuts over two years, that person said.

The Redskins technically did not violate salary cap rules but attempted to gain an unfair competitive advantage in subsequent years, which were subject to a salary cap, according to three people familiar with the league’s thinking.

Allen said in a written statement released by the team: “The Washington Redskins have received no written documentation from the NFL concerning adjustments to the team salary cap in 2012 as reported in various media outlets. Every contract entered into by the club during the applicable periods complied with the 2010 and 2011 collective bargaining agreements and, in fact, were approved by the NFL commissioner’s office. We look forward to free agency, the draft and the coming football season.”

Redskins officials declined further comment.

This season’s salary cap is $120.6 million per team, a figure that includes a redistribution to other teams — except the Raiders and Saints — of the deductions from the Redskins and Cowboys.

“All the clubs were warned not to do anything to create a competitive advantage when the salary cap came back, and that’s what [the Redskins] did,” said one of the people familiar with the matter. “They were very obvious about it. A lot of people were very angry about it. The ramifications could have been far worse for them. They could have lost draft picks. Some people recommended that to the commissioner.”

According to that person, the Redskins reworked some player contracts to pay them large sums during the uncapped 2010 season and save money against the cap in subsequent years. The person said the Redskins, in large part because of those maneuvers, had a player payroll far in excess of other teams’ payrolls.

Separately Monday, the Redskins released free safety Oshiomogho Atogwe and backup fullback Mike Sellers. They were scheduled to earn $3.4 million and $1.05 million, respectively.

Impact receiver a priority

After failing to produce a 1,000-yard wide receiver and managing only two plays in which a pass-catcher ran in for a touchdown last season, the Redskins’ top priority appears to be a playmaking wideout.

Fortunately for them, this year’s free agent class boasts good depth. The Redskins are expected to aggressively court San Diego’s Vincent Jackson, whom the Chargers are likely to let go rather than meet his contract demands.

The 6-foot-5, 230-pound Jackson is coming off a 60-catch, 1,106-yard, nine-touchdown season. He instantly would become Washington’s biggest and most explosive target.

But the competition for Jackson is likely to be intense. Eight teams may try to get him, including the Chicago Bears and Tampa Bay Buccaneers. The bidding could produce a contract that some in the league estimate could reach $12 million per year.

If the Redskins fail to lure Jackson, they could pursue New Orleans’s Marques Colston or Indianapolis’s Pierre Garçon. Speedy Saints wide receiver Robert Meachem also is an unrestricted free agent.

A starting right tackle ranks as the offense’s next biggest need. The team re-signed Jammal Brown to a five-year, $20.25 million contract last July. But the same hip that required surgery in 2008 and forced Brown out of the 2009 campaign continued to cause the seven-year veteran problems last season.

Brown has spent the offseason rehabilitating the injury, but Redskins officials still are expected to seek another right tackle. Seattle’s Paul McQuistan, who played in a zone-blocking scheme nearly identical to Washington’s, could be an option.

At left guard, Kory Lichtensteiger started last season and showed significant improvement over 2010. But in Week 6, he tore the anterior cruciate and medial collateral ligaments in his knee. The Redskins, who believe he will be fully recovered by the start of training camp, extended him a restricted free agent tender on March 2. But the team still could look for help, and Baltimore’s Ben Grubbs, who played for current Redskins offensive line coach Chris Foerster in 2007, may draw consideration.

With Rex Grossman a free agent and John Beck and Jonathan Crompton the only passers under contract, Washington may seek a veteran backup at quarterback. People familiar with the Redskins deliberations have named Kyle Orton as a target, but the likelihood of Griffin coming to town raises questions about whether a veteran with the opportunity to start elsewhere would want to join the Redskins.

Team wants Fletcher back

The top priority on defense remains re-signing inside linebacker and team captain London Fletcher. The soon-to-be 37-year-old will be entering his 15th NFL season, but has shown no signs of aging. Last season, Fletcher led the NFL with 166 tackles, recording three forced fumbles, two interceptions and 11 / 2 sacks. Coach Mike Shanahan and defensive coordinator Jim Haslett have stressed the importance of retaining Fletcher, who wants to stay with the team. But so far, the two sides haven’t agreed to a deal.

Allen said on Saturday that talks continue, and he remains hopeful that Fletcher will remain a Redskin. But Fletcher will hit the open market Tuesday afternoon unless Washington signs him before then.

“I had discussions with his agent over the last month or two,” Allen said. “We’ll see what happens. I’m not going hide . . . the fact that we love London. We hope he’s a Redskin.”

Defensive end Adam Carriker, who started at left end and is coming off a career season, also remains unsigned. Carriker said he wants to return to the Redskins, but also is excited about the interest he expects to draw in free agency if no deal is reached. Backup Jarvis Jenkins, who was out all of last season with a torn ACL, is expected to be at full speed for offseason workouts.

Strong safety LaRon Landry’s contract also has expired, but his ability to earn a new deal remains in question. Landry ended the season on injured reserve with an injured left Achilles’ tendon for a second straight season. He declined to have surgery that could have sidelined him for a year, and hopes to use alternative medicine to return to the form that had him in the running for defensive MVP in 2010. But he has yet to receive clearance to run.

The Redskins are wary of giving the five-year veteran a big contract because of the uncertainty about his health, and likely will wait to see how much interest Landry generates on the open market. Landry has said he might be willing to sign a one-year deal with Washington to prove that he has fully recovered in 2012, but that could change if another team is willing to gamble on him.

If Landry does not return, Washington could need a strong safety. Reed Doughty and DeJon Gomes both played strong safety last year, but the Redskins must consider whether either can get the job done on a full-time basis.

Although the Redskins have DeAngelo Hall and Josh Wilson at cornerback, it wouldn’t be surprising to see them make a run at another, because their defensive backs tallied only seven interceptions last season. The top corner on the market is Tennessee’s Cortland Finnegan, who figures to draw interest from a number of teams and reportedly wants to sign with the same team as his good friend Jackson.