Limbs-in-the-loch killer William Beggs has launched a legal battle against his conviction.
Murderer Beggs has launched a new legal wrangle
He was found guilty of murdering 18-year-old Barry Wallace following a Christmas works night out in Kilmarnock in 1999.
Beggs is claiming publicity about the murder made a fair trial impossible.
The hearing in Edinburgh is expected to last two days with the possibility that Beggs will then have to wait for a written ruling.
He is already three years into his life sentence.
The judge, Lord Osborne, ordered that Beggs should serve at least 20 years before even being considered for release.
Margaret Scott QC told Scotland's top judge, Lord Cullen - sitting with Lords Marnoch and Macfadyen - that Beggs should have the opportunity to contest some of the statements in the trial judge's report about the hearing.
Ms Scott argued: "Things are stated in the judge's report about Beggs which are disputed."
Beggs, 40, murdered Mr Wallace and then cut up his victim before dumping body parts in Loch Lomond and off the Ayrshire coast.
The killer, originally from Northern Ireland, picked up the teenager in Kilmarnock, took him back to his flat in the town and sexually assaulted him.
He later murdered Mr Wallace and dismembered his body.
Parts of Mr Wallace's body were found in Loch Lomond and his head was recovered from an Ayrshire beach.