U.S. senators from both parties reported some progress on Tuesday on a struggling proposal to create a $140 billion asbestos compensation fund, after some shuttle diplomacy by the plan’s author, Sen. Arlen Specter.

Specter believes he has met many of the concerns of Republicans about his draft bill, said Texas Republican Sen. John Cornyn, while Vermont Democrat Sen. Patrick Leahy said a bipartisan bill was a possibility.

“I feel more encouraged,” after talking with Specter about the asbestos compensation proposal, Leahy, the ranking Democrat on the Senate Judiciary Committee, told reporters. “I think we’re going to get a bill.”

Asbestos was widely used for fireproofing and insulation until the 1970s. Scientists say its inhaled fibers are linked to cancer and other diseases.

Hundreds of thousands of injury claims have forced dozens of U.S. companies into bankruptcy, including auto parts supplier Federal-Mogul Corp. and chemicals maker W.R. Grace & Co.

Specter, a Pennsylvania Republican and chairman of the Judiciary Committee, is proposing to take asbestos injury claims out of the courts and paying asbestos victims instead from a fund to be financed by business and insurers.

But his draft plan attracted little support from either party, clouding its chances of even getting out of committee. Last week, Specter met Republican members of the Judiciary panel to hear their concerns, and then went to talk to Democrats.

“He believes he has met many of the concerns that were articulated in the meeting with Republicans last Thursday,” Cornyn told reporters outside the Senate, adding that he hoped to see the changes in writing shortly.

“He (Specter) said he has worked with Senator Leahy to try to get Senator Leahy to support the bill,” Cornyn continued. “He’s apparently not there yet, but he’s hopeful that it would be a product that could get bipartisan support,” Cornyn said.

Cornyn said the $140 billion size of the proposed fund was not expected to change, adding that he could support that amount, “so long as it doesn’t get any bigger.”

Efforts to reign in asbestos claims are part of a broad Republican agenda, supported by President George W. Bush, to revamp the civil justice system.

But some Democrats like Leahy have also shown interest in an asbestos compensation fund, while stressing it must fairly compensate victims of asbestos-related diseases.

“I wouldn’t be working this hard if I didn’t think it was a possibility,” Leahy told reporters.

Among changes being discussed, Cornyn said, was taking away compensation Specter had proposed for smokers with no evidence of asbestos diseases, and using it instead to increase awards for those with verifiable asbestos diseases.

Cornyn said Specter also indicated he thought he had met the concerns of some Republicans that medical criteria for claimants should be tighter.