Kenneth R. Feinberg spent part of his summer barnstorming towns near the Gulf of Mexico, urging people who felt they had suffered financial hardship because of the oil spill to apply for a share of the $20 billion BP fund he was overseeing. The point of the fund was to pay claims rather than litigate them in court.

"It’s my opinion you are crazy if you don’t participate," Feinberg told a crowd at one stop in Louisiana.

And participate they did. Feinberg has seen applications that could bring a tear to the eye.

Others are likelier to raise eyebrows.

Take the businessman who explained that his part of the $20 billion fund should be … $20 billion. His income last year? Fifty thousand dollars.

A restaurant worker asked for $5.9 million in emergency payments, even though his earnings before the spill were just $18,000.

And then there are the 4,000 claims, using a one-page form letter, that flooded in from Plaquemines Parish a couple of weeks ago, some hand delivered to local claims offices.

They asked for grocery money, from $150 a month to hundreds of dollars, to make up for the fish they would have pulled from the gulf waters had there been no spill. Few offered any substantiation for the claim, though one person brought a dead fish.

In all, about 31,000 claims have little or no documentation, and the people who filed them have been asked to provide more information. And 1,000 more are "very, very suspicious," Feinberg said, and are being held for further examination.

"They’re not just sitting there," he said. "We can’t pay them without more documentation — minimal documentation, but enough to process the claim."

Suspicious claims are perhaps inevitable whenever a big fund is set up after a natural disaster.

The National Center for Disaster Fraud, formed in Baton Rouge after Hurricane Katrina, has prosecuted more than 1,300 cases arising from Hurricanes Katrina, Rita and Wilma, and has begun to take in tips about the oil spill as well.

"When these disasters strike, sadly, some small group of people will act with criminal intent," said Lanny A. Breuer, the head of the criminal division at the Department of Justice. Jim Letten, the U.S. attorney in New Orleans and executive director of the fraud center, said the center had already received "a little over 300" calls to the tip line about spill fraud.

"Individuals who simply make honest mistakes in the application process do not have to fear criminal investigation or prosecution," Letten said. But investigators "will actively pursue" anyone who commits intentional fraud, he added.

The fund has paid out on thousands of claims it has decided are legitimate. So far, 45,298 checks worth $824 million have been sent since Feinberg took over on Aug. 23.

Some plaintiffs’ lawyers are rankled by complaints about claims because they lack documentation. Stephen J. Herman, a New Orleans lawyer, called it "kind of ironic" to have Feinberg complaining about lack of documentation when he all but discouraged people from using lawyers to pursue their claims.

"If you’d had lawyers helping people fill out their claims forms, you’d probably have better documentation," he said.

The Feinberg team has handed nearly 100 of the most suspicious claims to private investigators for further inquiry and has begun the process of sending those that seem the most likely to be fraudulent to the Department of Justice.

Those familiar with the internal workings of the process provided details of some of the more questionable claims on the condition that those submitting the claims not be identified.

Some boat owners have submitted pay stubs for far more deckhands than they would seem to need to operate their boats (the investigators do look into the size of the fishing boats).

There was the restaurant worker who declared that his income had dropped after the spill, but it turned out the restaurant had closed before the spill. There is the shrimper whose documents showed his earnings in the year before the spill had been $90,000, but whose claim hit $2,066,000.

The team is also taking a close look at a person who appears to have developed a side business filling out reimbursement forms that appear to be consistently inflated.

Others appear to be trying to defraud victims. A law firm in New Orleans alerted Feinberg to reports of their clients getting letters from people claiming to work with Feinberg, using fake stationery and requesting wire transfer information that can be used for electronic theft.

"The American people have to understand that this underground economy down there is real," Feinberg said. "It’s a real problem for us."

Still, he added, some of what he sees — in particular, the one-page grocery requests — should not be thought of as serious fraud, but rather as attempts to "game the system."

"I don’t want to chill people from applying," he said.

Billy Nungesser, the Plaquemines Parish president, called the grocery claims "totally bogus" and suggested that the idea of submitting the them was "being circulated by some of the councilmen running for re-election."

That kind of talk angers Don Beshel, a Plaquemines councilman and the signer of several hundred of the forms, which he insisted he worked out according to the rules of the fund.

"It’s not up to me or anybody else who signed it to say the claim is valid, or invalid or anything," he said. "You can’t validate me giving somebody fish to put in the freezer."

John Barthelmy Jr., the principal of Phoenix High School in Plaquemines Parish, said he was surprised to find his name and various versions of the school’s letterhead on a number of the submissions for groceries.

He acknowledged that he signed some of the forms, but said he assumed that the idea that they could be submitted came from within the fund itself and not from the people of the parish. "We’re not that creative in the gangster area, to come up with that on our own," he said.

Preventing fraud and ironing out the remaining kinks in the process will be increasingly important as the fund moves from the first stage of emergency claims to the second, more complicated process of negotiating final settlements with people over their total losses from the spill.

That will be a process of long negotiation with a deadline three years away so that some of the long-term effects can at least be glimpsed and better predicted.

To Feinberg, the fundamental problem with paying the wrong people — it is not his money, after all — is protecting the victims.

Give in to fraud, and "the credibility of the program would collapse, the elected officials would scream, the American people would scream," he said. "It would become a grab bag.".

"The money would go away," Feinberg said. "The legitimate victims would suffer more as a result."