Lawyers for Facebook Inc. are trying again to settle a suit related to its “Sponsored Stories” advertising feature after a federal judge rejected an earlier proposal.

Lawyers for the social networking site submitted a new $20 million settlement late Friday that lets users apply for a cash payment of up to $10 each and drops a provision that would have set aside $10 million for plaintiffs lawyers’ fees.

In August, U.S. District Judge Richard Seeborg of San Francisco threw out a proposed settlement between Facebook and plaintiffs over claims that it illegally sold ads containing users’ likenesses, citing problems with a plan to donate $10 million to Internet privacy causes and pay $10 million in attorney fees.

Meanwhile, critics had also questioned why the settlement money wasn’t going to Facebook users, but to organizations that deal with consumers’ privacy rights, including the Electronic Frontier Foundation and The Center for Internet and Society at Stanford Law School.

The new agreement submitted to Seeborg would distribute any remaining funds to the charities, after users’ claims, attorney fees and other expenses are met. And if it’s not economically possible to pay all the users who submit a claim, the court can still decide to give the entire fund to charities. The proposed settlement covers nearly 125 million people, court documents show.

“We believe the revised settlement is fair, reasonable and adequate and responds to the issues raised previously by the court,” Facebook spokesman Andrew Noyes said in an emailed statement.

Richard Arnes, a San Francisco-based lawyer for the plaintiffs, did not respond to a request for comment.

Filed in 2011, Fraley v. Facebook, 11-1726, alleged that the social networking site’s “Sponsored Stories” feature violated California law by publicizing users’ “likes” of advertisers without any compensation or a way to opt out.

As part of both settlement proposals, Facebook also agreed to give users more control over how their names and likenesses are used. And Facebook’s revised agreement also gives parents more control over how their children appear in sponsored content.

But unlike the earlier settlement agreement, Facebook now has a right to object to plaintiffs lawyers’ fee applications.

And to support their settlement proposal, Facebook’s lawyers from Cooley pointed out in court documents filed Saturday that the U.S. Court of Appeals for the Ninth Circuit recently gave a stamp of approval to another Facebook privacy class action settlement that puts millions into a charity instead of giving money to plaintiffs. In September the Ninth Circuit surprised many when it upheld Facebook’s $9.5 million settlement of a suit that claimed the social networking site’s now defunct “Beacon” feature violated privacy laws. Before the ruling, judges such as Seeborg, as well as consumer and privacy groups, had expressed increasing skepticism about the fairness of similar class action settlements that dole out millions to privacy groups but not individuals.

Amy Miller is a reporter for The Recorder, a Legal affiliate based in San Francisco.