Private mediators have created a lucrative niche in recent years on the strength of their ability to resolve financial disputes more quickly and cheaply than the courts. Now come a couple of New York attorneys with a settlement mechanism so simple, quick and cheap that it could make a flesh-and-blood mediator weep.

Called CyberSettle.com, it is a Web-based service that compares numbers placed confidentially on the virtual table by the claimant and the insurer. If the two figures are within $5,000 or 30 percent of each other, a message pops up on the screen announcing, “Congratulations, you have a settlement,” splitting the difference between the two sides. If the offers aren’t within reach, neither party learns what the other had in mind, so neither will lose leverage in further negotiating.