As lawyers in the mammoth 9/11 respiratory litigation returned to the bargaining table Wednesday, they faced the daunting challenge of reaching an agreement that will satisfy Southern District of New York Judge Alvin K. Hellerstein.

Hellerstein stunned all sides in the case Friday when he rejected a proposed $575 million to $657 million settlement for those who responded after the World Trade Center terror attacks and cleaned up the site. The judge complained the settlement paid too little to victims and that its terms were confusing, making it difficult for some 10,000 individual plaintiffs to make a decision on whether to accept or reject payments.