BP Plc won’t seek to access Transocean Ltd.’s $750 million insurance policy for the Deepwater Horizon rig, which exploded while drilling a BP well in 2010, sparking the worst offshore spill in U.S. history.

London-based BP notified the Texas Supreme Court on Wednesday that the two companies resolved all differences over the drilling accident and spill in a confidential settlement reached May 20. BP withdrew its request for the state high court to reconsider its February decision that BP wasn’t entitled to Transocean’s insurance.

The U.S. appeals court in New Orleans bounced the case to the Texas Supreme Court in August 2013 for guidance on how to interpret the insurance policy under Texas law. Earlier, it sided with BP.

The Texas high court interpreted the policy and associated drilling contract in favor of Vernier, Switzerland-based Transocean, as had U.S. District Judge Carl Barbier of New Orleans, who oversees consolidated oil-spill litigation at the trial level. BP will also withdraw its appeal of Barbier’s ruling at the appeals court, according to the company’s filing in Austin.