The jury in the trial of a man convicted of killing four people in Pembrokeshire in the 1980s, were "profoundly misdirected", according to his legal team.
John Cooper, was convicted last year of shooting dead Peter and Gwenda Dixon on a coastal path in Little Haven, Pembrokeshire. He was also found guilty of murdering sister and brother Helen and Richard Thomas in their home near Milford Haven.
In today's hearing to decide if Cooper can appeal his life sentence his legal team claimed there was 'clear room for confusion in the jury's mind' during the trial.
The judgement has been reserved for two weeks.
Joanna Simpson was at the Court of Appeal in Cardiff.
Two of Wales's most notorious murderers, John Cooper and John Pope have had their appeals dismissed.
John Cooper will find out if he can appeal his life sentence for four murders in Pembrokeshire in the 1980s.