Former NFL players suffering from concussion-related problems are one step closer to receiving benefits as part of a $1-billion settlement with the NFL. A federal appeals court in Philadelphia on Wednesday rejected a motion for an en banc hearing requested by a small group of former players who had objected that the settlement was insufficient.

The decision means that the only recourse for the group protesting the settlement is to ask the U.S. Supreme Court to hear the case, but many legal experts believe the country’s highest court will not get involved in the matter. Once the appeals process is over, former players can begin receiving benefits as part of a settlement reached between the league and more than 5,000 former players who claimed in a lawsuit that the league had purposely hidden the dangers of concussions. The settlement was finalized in April.

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“We are pleased with the Third Circuit’s decision to deny the appellants’ requests for an en banc rehearing,” Christopher Seeger, co-lead counsel for the retired players, said in a statement Wednesday afternoon. “These objections have now been turned aside three times: by the District Court, a unanimous three-judge panel from the Third Circuit and the full Third Circuit without one judge dissenting.”

Seeger added he hopes former players, many of them suffering from neurodegenerative diseases caused by repeated blows to the head during their football careers, can now begin receiving benefits under a formula negotiated with the league and approved by the courts.

“These meritless appeals have come with devastating consequences for the thousands of retired NFL players suffering from neurocognitive injuries, and those concerned about their future, as they have been forced to wait even longer for the immediate care and support they need and deserve,” he said. “We hope these objectors will consider the over 20,000 retired players and their families that support this agreement before filing additional appeals to the U.S. Supreme Court that will only extend these delays further. We will continue to forcefully defend this important settlement should they decide to move forward with the appeals process.”