PHILADELPHIA -- A second petition has been filed asking the U.S. Supreme Court to reject the $1 billion settlement of NFL concussion lawsuits because of how it treats current brain injuries versus future ones.

The former players who filed the petition complain that chronic traumatic encephalopathy diagnosed before the April 2015 cutoff can bring $4 million while future CTE diagnoses aren't compensated. They say that violates Supreme Court rulings that insist each subgroup in a class action settlement be treated fairly.

The petition, filed Monday, echoes earlier complaints that the lead players' lawyers in 2013 signed with the NFL a quick deal that favored their clients over thousands of others.

Lawyers on the Plaintiffs' Steering Committee, who negotiated the deal, reject those arguments and say the appeals are holding up payments that ailing retirees need. The NFL declined to comment on Wednesday.

The 31 petitioners include a number of men who played for the Dallas Cowboys, including 1996 Super Bowl MVP Larry Brown and Hall of Famer Charles Haley.

Washington lawyer Deepak Gupta, who represents them, said the Supreme Court had not reviewed a case involving the disparate treatment of subgroups within a class action case in about 20 years. Meanwhile, he said, the federal appeals court in Philadelphia that upheld the NFL settlement has a different view of the issue than its counterpart in New York. That could pique the Supreme Court's interest.

According to the petition, the family of former Chicago Bears safety Dave Duerson, who was found to have CTE after his 2011 suicide, can seek an award of up to $4 million while the family of former Oakland Raiders quarterback Ken Stabler, whose CTE was diagnosed after his July 2015 death, cannot.

CTE, a degenerative disease found in people such as boxers and other athletes who've suffered severe hits to their heads or repeated concussions, currently can be diagnosed only at autopsy, although scientists hope to diagnose it in the living within the next decade.

The settlement covers future cases of Alzheimer's disease, Parkinson's disease, Lou Gehrig's disease and dementia but not CTE.

"Seeking to head off a tsunami of future claims," Gupta wrote in the petition, "the NFL pushed for a global settlement of all current and future claims -- while compensating only current CTE claims."

Supporters of the settlement say it compensates future cases of dementia. But the payout for dementia is expected to average $190,000, compared with $1.44 million for CTE, the petition said.

Gupta and other critics also complain the plan does not compensate the depression, mood swings and memory loss they consider precursors to dementia and a CTE diagnosis.

The family of former Buffalo Bills fullback Carlton "Cookie" Gilchrist filed the only other Supreme Court petition. The deadline has now passed. It could be months before the court decides whether to hear the case.

The Plaintiffs' Steering Committee lawyers on Wednesday pointed to the 3rd U.S. Circuit decision that found the award scheme "fair, reasonable and adequate."

"The Fund is uncapped and inflation adjusted, protecting the interests of those who worry about developing injuries in the future," the judges wrote in April.

The settlement would resolve thousands of lawsuits that accuse the NFL of hiding what it knew about the risks of football concussions. The settlement, overseen by Senior U.S. District Judge Anita B. Brody, is designed to cover about 21,000 retirees.