INVERNESS, Fla. -- The two children of Ted Williams who want his body kept frozen are trying again to reach a compromise with their half sister, who says the baseball great should be cremated.

John Henry Williams and his sister, Claudia, asked a state court judge Wednesday to order a mediation session with their half sister, Bobby-Jo Williams Ferrell. They hope to avoid a public showdown in court.

"John-Henry and Claudia feel strongly that the disposition of their father's body is a private matter,'' their attorney, Robert Goldman, said in the motion.

Williams died July 5. He was 83.

Williams' children already have tried mediation, negotiating for hours Monday, but were unable to reach agreement.

"We believe a second meeting could very easily result in a common understanding of Mr. Williams' wishes and moot the need for a judicial resolution,'' the motion said.

Ferrell's attorney, Richard Fitzpatrick, said an agreement is possible.

"There's middle ground everywhere,'' Fitzpatrick said. "Now this is a very difficult case to find that -- I agree with that -- but I'm not about to say there's no possibility that there couldn't be any middle ground.''

Ferrell has accused John Henry Williams of sending their father's body to the Alcor Life Extension Foundation in Arizona so he could profit off their father's remains or sell his DNA.

"One point should be made clear,'' Goldman said at a news conference. "Claudia and John Henry Williams will never profit off of their father's body or the disposition of their father's remains.''

Cryonics advocates say science might one day be able to thaw a body, cure whatever killed the person and restore life. Most experts say that's highly unlikely.

If no agreement is reached, a judge could decide whether Williams wanted to be frozen or cremated. The Hall of Fame outfielder's will and the executor of his estate present conflicting accounts of his intentions.

In the will that was filed and made public Tuesday, Williams said he wanted his ashes "sprinkled at sea off the coast of Florida where the water is very deep.''

Williams also specified he didn't want a funeral or memorial service.

But executor Albert Cassidy said that after Williams wrote his will on Dec. 20, 1996, he expressed a desire to have his body frozen.

Along with the will, Cassidy filed a petition asking a judge to decide what should be done with the body.

John Henry Williams and Claudia Williams, in a separate filing Wednesday, asked that the petition be dismissed since Cassidy had no responsibility over Ted Williams' body as executor. They also argued that the court in Citrus County lacked jurisdiction over Williams' body since it is no longer there, and wills don't control what happens to bodies.

"John-Henry Williams and his sister had authority to cryonically preserve Mr. Williams,'' the filing said. "Mr. Williams' final wishes were that he be cryonically preserved.''