"I don't understand why you want a treaty where the best interests of the child are what's at issue, and then you interpret it in a way that the court of one nation with the child where you have parents from both nations pays no attention at all to what courts in other nations are saying."

Jeff Chafin was in the courtroom for the morning arguments, dressed in his Army dress uniform.

"I told my little girl I would do everything I could to get her," Sgt. Chafin told CNN National Correspondent Joe Johns this week, "to make sure she's safe." He last visited the girl overseas a few weeks ago.

"I don't believe that (the current legal fight) is in the best interest of the child as it's going to go on for years and years to come," Lynne Hales Chafin told CNN.

A ruling is due in a few months. The case is Chafin v. Chafin (11-1347).