The Dallas Cowboys are unlikely to challenge the NFL’s decision to cut the team’s salary cap space by $10 million over the next two seasons, a person familiar with the case said Thursday.

That would leave the Washington Redskins, who lost $36 million in cap space in the same decision, to act alone if they choose to challenge the NFL’s ruling. The case centers on the way the two teams structured some player contracts in 2010.

It remained unclear Thursday whether the Redskins would contest the league’s decision, either via an appeal to the NFL or a legal challenge. Several people familiar with the case said in recent days that the Redskins were considering their options, though the team declined to comment Thursday.

The person with knowledge of the case said Thursday that the Cowboys probably would do nothing but that the Redskins “might be considering some legal options.”

It was unclear, the person said, whether the Redskins “want to take that on” because of the possible ramifications of challenging a league decision in court. The Redskins could risk further alienating other teams and league officials, the person said. Another person familiar with the case said earlier this week that some in league were angry enough about the Redskins’ actions that they had urged NFL Commissioner Roger Goodell to strip draft picks from the team. Instead, the league decided on the salary cap reductions for the Redskins and Cowboys.

The league concluded that the Redskins and Cowboys attempted to gain an unfair competitive advantage by the way they structured players’ contracts in 2010, when the sport had no salary cap. However, the Redskins technically committed no violation of salary cap rules.

The Redskins reworked contracts to pay players millions of dollars during the uncapped season that otherwise would have been paid in subsequent seasons when the salary cap was back in effect. That way, the money did not count against the salary cap and the Redskins cleared cap space for other seasons.

The NFL found that the Cowboys were guilty of similar tactics, but to a lesser degree, people familiar with the case have said.

Both teams have denied wrongdoing. The Redskins, in a written statement earlier this week, said they complied with the NFL’s labor contract and that all of their player contracts were approved by the league office.

A person familiar with the NFL’s thinking in the case said earlier this week that the league had no basis to reject the contracts at the time but feels it did have a basis to take action this week, given the overall approach taken by the Redskins.

The $46 million in salary cap reductions were redistributed to 28 of the other 30 NFL teams and are part of this season’s salary cap total of $120.6 million per club. The NFL Players Association deliberated with the league for a week over the reductions and reluctantly agreed to them, a person familiar with the union’s thinking said earlier this week.

The Redskins must absorb at least half their salary cap reduction this year, according to multiple people familiar with the case. That hasn’t stopped the team from adding players in free agency, including wide receivers Pierre Garcon and Josh Morgan and safety Brandon Meriweather.

But there have been some apparent salary cap considerations in those maneuvers. Morgan signed a five-year contract that can be converted to two years, according to people familiar with the contract. That deal lessens the initial salary cap impact because the contract’s bonus is prorated against the cap over five seasons instead of two.

More on the salary cap hit:

Jenkins: Snyder’s fault

Hamilton: I’m on Snyder’s side

Redskins’ methods drew league anger

Hard Hits: Another costly mistake