Judge Barbier, who would hear the case without a jury, has issued pretrial rulings limiting the scope of the vast amount of evidence collected — more than 300 plaintiffs’ lawyers have produced tens of millions of pages of documents, thousands of exhibits and hundreds of videotaped depositions. The judge said he would not entertain testimony about previous BP accidents. He has also opened the door for punitive damages for some plaintiffs.

Of those still in the pool of plaintiffs, several who sat for a recent interview in their lawyer’s office said that they would have preferred to settle, but that they had gotten no satisfaction from the compensation fund, administered by Kenneth R. Feinberg, a lawyer in Washington.

Glenn Poche, a shrimper, said he had lost 90 percent of his retail business. Despite official assurances that seafood pulled from the Gulf of Mexico is safe, many of his customers “want to wait a couple more years” to be sure.

Kenneth Bundy, who owns a commercial dock where Mr. Poche sells his shrimp, said he had received $25,000 from the fund, but no payments to cover his continuing losses. His son, Grant, who manages the dock, has not received a settlement offer and is getting by financially by working a side job at a small seafood business. “If we don’t get some money from somewhere, we’re going to be out of business,” Kenneth Bundy said.

Diane Poche, Glenn Poche’s wife, said she had received $30,000 from the fund — “just a little drop in the bucket of what we’ve lost” — but her claims for more had been refused, she said, her voice rising. “I sent in paperwork over two inches thick!”

The Poches’ claim has been championed by Senator David Vitter of Louisiana, who wrote to Mr. Feinberg last year. In his response, Mr. Feinberg said that the Poches’ claim was for more than twice the annual gross income Mr. Poche had reported before the oil spill and that Mrs. Poche was listed as a housewife, not a business partner, on the family’s tax forms. Mr. Feinberg has said that thousands of claims have been rejected because of inadequate documentation.

Professor Uhlmann suggested that “claims that are weak may fare even worse in court, where the burden of proof will be on the plaintiffs.”