In a last ditch effort to avoid potentially dishing out billions of dollars, three companies have asked a Rhode Island judge to order a mistrial in a case that found the former lead paint manufacturers liable for creating a public nuisance.

In 2002 Rhode Island sued several companies that had manufactured lead paint, claiming their products created a public nuisance by contaminating thousands of homes. Despite the fact that the companies manufactured the paint decades earlier and the state was unable to identify which companies' products were responsible for the contamination, the state claimed the manufacturers should be liable because the paint continues to poison children. A jury found the companies liable, but at press time the judge had yet to decide the amount of damages, which some say could total billions of dollars.

The defendants, Sherwin-Williams Co., Millennium Holdings LLC and NL Industries Inc. claim that the state presented no evidence at trial that could connect the companies to the lead paint contamination.

“The result is that three, out of many historic manufacturers, were held liable for harms that were scientifically unknown and unknowable at the time of manufacture–all without showing that a single drop of lead pigment present in Rhode Island today was, in fact, made or distributed by any of the defendants,” the filing said.

This is the second time this case has come before Rhode Island courts. In October 2002, the first trial was declared a mistrial.