SAN FRANCISCO — For the second time, lawyers for Facebook Inc. asked a federal judge on Thursday to sign off on a $20 million settlement in a class action over its “Sponsored Stories” advertising feature.

In August U.S. District Judge Richard Seeborg of San Francisco rejected a proposed deal between Facebook and plaintiffs that provided for $10 million in charitable donations and up to $10 million in attorney fees, but no monetary benefit to class members.

This time there’s cash for claimants, up to $10 per individual, and no funds revert back to the social networking company. The new settlement also deletes a “clear sailing” provision, which would have barred Facebook from opposing the fee requests made by plaintiffs counsel.

Seeborg, who has been operating amid mixed signals from the U.S. Court of Appeals for the Ninth Circuit, did not rule immediately. However, he seemed inclined to approve the revised settlement.

“You certainly endeavored to address the concerns, which were serious concerns on my part,” Seeborg said.

Fraley v. Facebook, 11-1726, alleged that Facebook’s “Sponsored Stories” violated California law by publicizing users’ “likes” of advertisers without any compensation or method to opt out.

The settlement covers a class of roughly 125 million Facebook users and lawyers have suggested the volume of claims could make distribution impractical. Under the settlement agreement, Seeborg can decide to give the entire fund to designated privacy organizations if individual shares dip below about $5.

Lead Facebook attorney Michael Rhodes of Cooley and San Francisco plaintiffs lawyer Robert Arns both touted privacy safeguards in the new agreement that give Facebook users more control over the use of their names and pictures.

These are “real tools,” not “fictional tweaks,” Rhodes told Seeborg. Rhodes also referenced a September ruling from the Ninth Circuit in Lane v. Facebook, 12 C.D.O.S. 10846. The 2-1 decision upheld a $9.5 million settlement agreement distributing millions of dollars to privacy groups, but not to individual class members. Seeborg had approved the settlement in that case, which involved another Facebook advertising program.

The decision followed a string of rulings critical of so-called cy pres settlements that dole out money to charities rather than class members. Objectors to the Lane settlement have petitioned for en banc review, Seeborg noted.

Rhodes, also counsel in that case, said he is preparing Facebook’s opposition. “I appreciate you keeping abreast of my practice,” he quipped.