Calling it a "significant improvement" over an earlier proposal, a federal judge in Philadelphia granted preliminary approval Monday to the NFL's second settlement offer to former players who sued the league over concussion-related health problems.

The move came six months after U.S. District Judge Anita Brody rejected the first deal put forth by the league. It opens the door for more than 20,000 of the NFL's potentially eligible retirees to pursue claims as part of the class-action settlement.

If the majority of players opt in, the deal could spare the league years of protracted litigation over allegations that its executives hid or ignored evidence that concussions can cause brain damage with long-lasting health implications.

The NFL has annual revenues approaching $10 billion, and critics of the deal have said the league is getting off lightly.

In an opinion released Monday, Brody cited the league's elimination of a $675 million cap on payouts to players with neurocognitive disorders as key to easing the concerns that led her to reject the first settlement proposal in January.

"The parties have satisfied my concern on this fundamental issue," she wrote.

Whether that step will be enough to convince dozens of players who have spoken out publicly against the settlement remains uncertain. Last week, seven former players, including former Eagles wide receiver Sean Morey and safety Sean Considine, signaled in court filings that they might opt out.

"The revised settlement is a great deal - for the NFL and class counsel," lawyers for the seven players said in court filings. "It is a lousy deal for the retired players, whose rights have been bargained away without adequate or independent representation."

However, Christopher Seeger and Sol Weiss, lawyers appointed to lead the negotiations on behalf of the more than 4,500 who have filed suit so far, remained bullish Monday that most of the eligible players would buy in.

"We have received overwhelming support from the retired player community as they learn more about the guaranteed benefits and long-term security this settlement provides. We look forward to soon finalizing this agreement," they said in a statement.

Among the players who filed suit were former Chicago Bears and Eagles quarterback Jim McMahon, who suffers from dementia, former Eagles fullback Kevin Turner, and Hall of Fame running back Tony Dorsett.

Anastasia Danias, an NFL senior vice president, thanked Brody in a statement "for her guidance and thoughtful analysis of the issues as reflected in the comprehensive opinion she issued."

Under the terms that Brody approved Monday, retired players would be compensated on a sliding scale based on age, the number of seasons played, and whether post-career injuries might have contributed to their diagnoses.

Maximum awards of $5 million would go to players under 45 who played five or more seasons and require extensive treatment over their lifetimes for conditions such as Parkinson's disease or Lou Gehrig's disease.

Payouts decreasing on a scale would be provided for older players or those who played fewer seasons and had less serious health issues.

The terms of the new offer will be sent to all eligible retired players and their beneficiaries. They can then decide whether to opt in, object to its terms at a hearing scheduled for Nov. 19, or reject it outright.

Brody rejected the initial settlement offer in January, saying she was not convinced that the league had put up enough money to cover the 65-year life span of the deal. That proposal would have created a $765 million fund for cash awards to players, medical testing and education on concussion-related injuries.

Seeger and Weiss said at the time that they were confident in their projections that $675 million earmarked for player claims would be enough.

But the lawyers realized early on that the judge was unlikely to approve the deal without significant renegotiation, according to attorneys close to the negotiations.

"As soon as she rejected it, it was clear this wasn't about persuading Judge Brody that our numbers were right," said Craig Mitnick, a Haddonfield attorney who has traveled across the country educating former players about the settlement. "It was about ensuring that no matter what, the numbers would be enough."

Even with the removal of the cap on payouts, lawyers for the players and those representing the NFL said Monday they did not expect claims for damages to exceed the $675 million sum they originally projected.

In exchange for the cap's removal, the league insisted on additional safeguards to protect itself against fraudulent claims. The new deal allows the NFL to contest an unlimited number of requests for awards.

The new deal also would create a network of approved doctors for former players seeking to collect along with tightened requirements on physicians making those diagnoses.

"The deal provides more financial compensation for the players. It provides more benefit for the players," Mitnick said. "And the NFL gets this huge monkey off their shoulders."