Tom Benson’s efforts to win back a measure of privacy amid a messy public squabble with his estranged relatives over the future of his business empire hit a snag Wednesday.

A federal magistrate judge overseeing one of the fistful of lawsuits touched off by the dispute declined to grant a request that he impose a gag order in the case. Benson’s lawyers had asked for the order to keep sensitive financial information from slipping into public view.

A testy U.S. Magistrate Judge Joseph C. Wilkinson Jr. told Benson’s lawyers the motion was premature and said, “We’re not going to have a record you sometimes see around here where everything is filed under seal and you can’t tell what’s on the record.”

He added, “We’re not going to have chaos in this case, and it won’t degenerate into a circus.”

Though Wilkinson made no explicit mention of the other lawsuits involving Benson and his relatives, his ruling came just a day after Civil District Court Judge Kern Reese decided that a June 1 trial in his courtroom over the 87-year-old Benson’s mental fitness will be closed to the public.

In that case, Benson’s former heirs are trying to get him declared unfit to make major financial decisions. They made the request after being cut out of his succession plans for the Saints, Pelicans and other businesses earlier this year.

The matter before Wilkinson has to do with a group of family trusts containing non-controlling shares in the city’s NFL and NBA franchises. Benson is seeking to remove those assets from the trusts and replace them with other assets of equal value.

He will have to complete the swap to remove his daughter Renee Benson, granddaughter Rita LeBlanc and grandson Ryan LeBlanc from any future involvement with his businesses.

The swap was held up earlier this year by Robert “Bobby” Rosenthal, one of the stewards of the trust funds.

Rosenthal rejected a proposal from Benson to replace the shares with $449 million in secured promissory notes, the cancellation of $94.5 million worth of debt and some real estate. He said he could not accept the deal before Benson provided an updated valuation of the trust’s assets, which had not been completed.

Benson’s lawyer, Phil Witt-mann, told the court Wednesday that the valuation is now complete, though he would not provide even ballpark figures.

While he declined to implement a blanket gag order in the case, Wilkinson said it might be appropriate to seal court filings that contain financial details concerning the proposed swap. But he said it would be premature to start shielding the court record before those details come up.

At the moment, Rosenthal is still challenging whether the federal court in New Orleans is even the right jurisdiction for the case, given that he lives in Texas.

“If you want (something) under seal, submit evidence to establish it is proprietary or commercially sensitive, and show that the private interest outweighs the public interest,” Wilkinson said.

Lawyers for Rosenthal have said he would be open to a gag order on financial details in the case if it continues in New Orleans.

Rosenthal is not the lone defendant in the case. Last month, Texas lawyer Mary Rowe became a co-defendant after agreeing to oversee some of the trusts involved. As of Wednesday, an attorney representing Rowe hadn’t made a first appearance in the case.