Ian Bailey's lawyers are back in the High Court today as part of their bid to secure an appeal against his extradition to France.
The French authorities issued the warrant for the purpose of prosecuting the journalist for the murder of film producer Sophie Toscan du Plantier in West Cork.
Mr Bailey wishes to appeal his extradition but to even get to the Supreme Court first he has to show his case raises points of law of exceptional public importance.
Last week, his legal team indicated they had three grounds of objection to the High Court order permitting his surrender to the French authorities.
In his decision, Mr Justice Michael Peart said the warrant was clearly issued for the purpose of prosecuting the journalist for murder and there was nothing to show he would not receive a fair trial in France.
Mr Bailey has always denied any involvement in the killing of the French film producer who was found beaten to death near her holiday home in Schull more than 14 years ago.
The DPP has not pressed charges against him.