Bill Eddins, a certified mediator, said the bargaining over the fate of Alex King, 13, and Derek King, 14, would resume Wednesday and that is likely to be the last session.
"I can report to you that we met yesterday for several hours in both joint and individual sessions," Eddins said. "Everyone worked hard and participated fully. We have recessed the joint session until next Wednesday at 9 o'clock and hopefully that will be the final session.
"We anticipate the negotiation will be concluded -- either way -- at that time," he said.
Mediation is common in civil lawsuits, but it is rare in criminal cases, especially murder trials.
The boys' second-degree murder conviction was thrown out by Circuit Judge Frank Bell on Oct. 17 on grounds the boys were denied due process.
The mediation could determine what punishment will be given to the young teens, who had faced the possibility of 20 years to life in prison.
Alex and Derek King were convicted Sept. 6 of second-degree murder without a weapon. Jurors said they believed the boys did not actually kill their father, 40, but allowed their friend Ricky Chavis, 41, into the house and he did it.
Chavis, a 41-year-old convicted child molester who allegedly had been having sexual relations with the younger brother, had also been charged with the murder. But a different jury had acquitted him a week before the boys' trial. The verdict had been sealed and was read after both verdicts had been reached.
Many of the jurors in the boys' trial were upset when they learned Chavis was found innocent. They had concluded that Chavis did the killing, and the boys let him into the house to do it.
The boys' attorneys -- James Stokes, Sharon Potter and Dennis Corder -- used comments by jurors to seek a new trial, and Judge Bell threw out the verdict.
If mediation fails, the boys' attorneys are likely to be replaced. Entertainer Rosie O'Donnell hired a celebrity lawyer, Jayne Weintraub, to assist the boys' case.
The boys' mother, Kelly Marino of Lexington, Ky., said she was not happy with the current attorneys' performance at the trial.
"I'm not trying to make trouble; I'm just trying to do what's best for my children," Marino said.
Weintraub clashed with the defense team and is not taking part in the mediation.