Five weeks after taking over the oil spill damage claims from BP, and after widespread criticism of delays in processing applications, claims czar Kenneth Feinberg said his operation had eliminated the backlog of older claims that had been sitting in the system unpaid.

“There is virtually now no backlog,” Feinberg told us this morning. “We are now current with any of the older claims.”

The latest statistics from his operation indicate that nearly 39,000 claims have been paid or approved, another roughly 27,000 have been flagged for inadequate documentation, and almost 8,700 are under review. “The only backlog we have now in the system," Feinberg said, "is claims that have come in over the last few days,” as well as the large number of insufficiently documented claims that he said his organization is unable to process.

However, some applicants in our BP Claims Project said that their claims are still waiting in limbo even though they filed with Feinberg’s operation more than a month ago. (If you filed a claim with Feinberg’s organization, you can tell a reporter if you’ve been paid yet using this quick online form.)

Marcia Mandel, who filed a claim on Aug 24 for lost income on behalf of her hotel, the Marco Island Lakeside Inn, said that her application was still under review. She said she had been told by Feinberg’s organization that her documentation was complete, but that even after sending them disconnect notices from the water and electricity companies last week, she had not gotten a decision.

“Saying the backlog is gone is nonsense,” Mandel said.

Other claimants, in telephone conversations and comments on our website, reported that they had gotten paid in the last few days, but not always for the amount that they had requested.

Feinberg said that his organization’s progress in paying claims came from increased efficiency, and that his operation was “now turning over in excess of 2,000 claims a day.”

But for those whose claims are still outstanding, Feinberg’s statement that the backlog had been eliminated raised more questions than they answered. Jon Faulkner, who filed a claim on Aug. 25 for lost wages as a charter boat skipper, said that he had been assured by Feinberg’s operation that his claim was complete, but that he was still awaiting a response.

“They assured me there’s nothing wrong with my claim, but I haven’t heard from them,” Faulkner said. “I don’t know if I’ve fallen through the cracks.”