Plaintiffs' attorneys who brokered a multibillion-dollar settlement with BP following the company's 2010 Gulf oil spill have asked a federal appeals court to uphold a judge's approval of the deal.

Only a "paltry few objectors" have raised the "narrowest of concerns" about the settlement that U.S. District Judge Carl Barbier approved in December 2012, private lawyers said in a filing Tuesday with the 5th U.S. Circuit Court of Appeals.

"None of them complain of their compensation calculations, identify what compensation they are entitled to under the Settlement, or define what other or greater compensation they believe they should receive," the attorneys wrote.

On Friday, BP attorneys argued that a three-judge panel of the 5th Circuit should overturn Barbier's approval order if the company's separate appeal of more recent rulings on settlement terms is unsuccessful. BP argues that Barbier misinterpreted the settlement and has allowed businesses to receive hundreds of millions of dollars for inflated or fictitious claims.

A different 5th Circuit panel heard the company's appeal in July but hasn't ruled yet. BP said it would still support Barbier's approval of the settlement if its appeal is successful.

Although Tuesday's brief doesn't explicitly address that dispute, plaintiffs' lawyers said BP initially was "thrilled" with how claims were being processed. They previously have argued that BP undervalued the settlement and underestimated how many claimants would qualify for payments.

Court-supervised claims administrator Patrick Juneau's office has made more than $4.5 billion in settlement offers to more than 55,000 Gulf Coast businesses and residents who claim the spill cost them money.