PHILADELPHIA — Retired NFL players who sued the league over on-the-field concussions have overwhelmingly accepted a multimillion-dollar settlement despite serious misgivings about some of the terms, lawyers representing the players said Tuesday.

Tuesday marked the deadline for players to agree to opt out or object to the terms of the settlement, before a Nov. 19 fairness hearing in the case.

“The deal has overwhelming support of the player community,” said Christopher Seeger, the lead lawyer representing retired players.

U.S. District Judge Anita Brody granted preliminary approval to the deal in June after the NFL agreed to remove a $675 million cap on payments. Brody refused to sign off on the earlier deal because she worried the money set aside by the NFL would be insufficient.

Under the revised terms, payments of up to $5 million will be guaranteed to any retired player who develops the neurological impairments, including Alzheimer’s disease, Parkinson’s disease and amyotrophic lateral sclerosis, widely known as Lou Gehrig’s Disease.

Payments will be based on a formula that considers years played in the league and the players’ age at diagnosis. The fund is set to last 65 years from when it is authorized.

“It is nowhere near the deal it should be,” Jason Luckasevic, an attorney who filed the first concussion case against the NFL, told Reuters.

Despite the concerns, Luckasevic estimated that only two dozen of his 525 clients would opt out of the deal, freeing them to sue the NFL on their own.

Despite the widespread acceptance, there remain pockets of serious concern.

One group of players has asked to modify the deal, arguing it arbitrarily cuts off payments to those who are diagnosed with a condition known as chronic traumatic encephalopathy, or CTE, which is caused by repeated blows to the head and can lead to aggression and dementia.

Under the current deal, the NFL will pay $4 million to the families of men who died from CTE before July 7, 2014. Those diagnosed afterward receive nothing.

“It makes no sense,” Steven Molo, a lawyer representing seven former players or their families, said of the CTE issue. “There’s a whole group of people being excluded from any meaningful benefit.”

The ability to diagnose CTE before a patient dies is only an emerging science.

The settlement will affect about 20,000 retired NFL players, but analysts estimate that just 12,500 will participate.