(FORTUNE Magazine) – A solution to the 20-year-long asbestos mess may finally be in the works. As FORTUNE explained last March (see "The $200 Billion Miscarriage of Justice" on fortune.com), trial lawyers have pitted plaintiffs who aren't sick against businesses that never made asbestos. Now, as companies like Honeywell and Halliburton negotiate private settlements, leaders of the largest business groups have decided to cooperate, which increases the odds of a global settlement within the next two years.

In November representatives of such groups as the U.S. Chamber of Commerce, the National Association of Manufacturers, and the Business Roundtable met to urge companies beset by suits to unite. Soon talks began between the warring factions--one mostly composed of companies ravaged or bankrupted by asbestos suits (Owens Corning, W.R. Grace) and a second representing companies like GE, GM, Ford, and Dow Chemical that fear rising asbestos liabilities. If the negotiations lead to a single proposal, and insiders assert that they will, Congress will be more willing to step into the morass and legislate.

The term "morass" is an understatement. Claims for asbestos-related illnesses reached 600,000 in 2000 and have been rising by 50,000 a year. The cost so far is $54 billion; the total could reach $275 billion. Sixty-one companies have been bankrupted, one-third in the past two years. And most new claims are coming from people who aren't yet sick.

The business factions disagree on who should pay. Bankrupt or near-bankrupt companies want to put off claims and reduce the number of suits by using American Medical Association criteria to determine who is ill. Sick workers would be eligible for a payout; those who aren't could sue if they do get sick, with no statute of limitations. The group including GE and GM favors capping asbestos liability, paying now to create a trust fund, and putting the mess behind them. Because devising a trust fund will be hard--how large is large enough?--the medical-criteria proposal will likely be the starting point.

The new chairman of the Senate Judiciary Committee, Orrin Hatch, has made curtailing asbestos lawsuits a priority; James Sensenbrenner, who chairs the House panel, says he'll "hot line" whatever the Senate passes. One reason Congress may act is that during the midterm elections, insurers helped bankroll $2 million in TV, radio, and print ads that decried runaway asbestos litigation. The ads ran in states like Nebraska, Wisconsin, and Washington, where business interests hoped to win over moderate Democrats whose votes will be crucial to curtailing the lawsuits. The insurers also hired Democratic lobbyists John Podesta and Harold Ickes, late of the Clinton White House, to convince labor unions that their interests aren't with their usual allies, the trial lawyers.

President Bush would support any plan that gains momentum in the business community and Congress. He, too, would love to beat the lawyers.