SAN FRANCISCO — The Heller Ehrman estate and Greenberg Traurig have agreed to pursue mediation in one of the most significant claims remaining in the defunct firm’s four-year-old bankruptcy case.

The Heller estate filed suit against Greenberg in U.S. Bankruptcy Court in October 2011 over conduct that allegedly cost the estate millions. Staring down a grueling deposition schedule that involves more than 20 witnesses scattered across the country, the parties decided to try to resolve the suit before running up even more expenses through the deposition process, according to a joint stipulation filed Wednesday.