Victims of phone-hacking by News Corp.’s now-defunct News of the World tabloid dropped plans to seek additional damages designed to punish wrongdoers at a civil trial next year.

Pursuing exemplary damages could prejudice the criminal proceedings, scheduled to begin in September 2013, a few months after the civil suit is scheduled to start, Hugh Tomlinson, a lawyer for the victims, said at a hearing in London today.

“It’s in the best interests to remove the plea of exemplary damages on the basis that the claimants will be fully and properly compensated by awards of ordinary and aggravated damages,” Tomlinson said.

News Corp., controlled by Rupert Murdoch, has paid out more than $315 million for legal fees, civil court settlements, and the cost of shutting the News of the World as a result of the phone-hacking scandal. It continues to be the subject of police probes into phone and computer hacking and bribery.

“We are glad that the claimants have very sensibly seen the light and agreed to the proposal that they should abandon their claim,” News Corp. lawyer Dinah Rose said today.

The civil lawsuits are being handled as a single case to establish a common set of claims and facts about the hacking conspiracy and set standards for monetary damages. A trial scheduled for February 2012 was canceled after victims were paid as much as 600,000 pounds ($972,000) each, including costs.

The current civil trial, which had been scheduled to begin in May, could be pushed back until June, Judge Geoffrey Vos said today.