Lawyers for New York City, its contractors and plaintiffs huddled Thursday with special masters in an attempt to reframe a settlement that will satisfy Southern District Judge Alvin K. Hellerstein in the litigation involving respiratory illnesses allegedly caused by toxic dust at the World Trade Center site.

The meeting among the lawyers and special masters Aaron D. Twerski and James A. Henderson came before what had been scheduled to be a full fairness hearing Monday on a proposed $657 million settlement that could cover up to and beyond 10,000 plaintiffs.