Brian Boyle and Greig Maddock were both given life sentences
Scotland's most senior law officer has called for the country's worst killers to face sentences that could see them die behind bars.
Lord Advocate Elish Angiolini QC wants appeal judges to increase the upper limit of the minimum jail term which must be served by murderers.
The Crown has taken the cases of three men convicted of murder to the Court of Criminal Appeal in Edinburgh.
It claimed that the sentences they received were "unduly lenient".
Anyone convicted of murder gets an automatic life sentence, but the sentencing judge has to fix a period - known as a "punishment part" - which must be served prior to the killer becoming eligible to apply for parole.
The punishment part of the sentence was brought in following the adoption of the European Convention on Human Rights and informs the murderer of the minimum time he or she must serve in jail.
Mrs Angiolini told the court that an appeal case in 2002 had led to an understanding that the range of punishment parts available to reflect the seriousness of the crime was "a relatively compressed scale from 12 years to 30 years".
In the benchmark case, former Royal Scots corporal Andrew Walker, who gunned down three people in an Army payroll robbery, had his minimum term reduced from 30 years to 27 years.
Mrs Angiolini said: "As lord advocate I consider that is inadequate to reflect the wide range of conduct which may amount to murder and fails to reflect adequately the exceptionally serious cases of murder, particularly those involving multiple victims, terrorism or persistent sexual violence against vulnerable adults or children.
"I am asking the court to consider issuing a guideline opinion which will recognise that 30 years is not the absolute maximum punishment part and recognises explicitly that in some exceptional cases a punishment part which exceeds the natural life expectancy may be appropriate."
The lord advocate told the court that she was not seeking "a rigid tariff scheme" but wanted more detailed guidance for judges sentencing in murder cases.
She maintained it would enhance public confidence that judges were being consistent in their approach to dealing with murder cases.
In other jurisdictions, such as England, the worst cases of murder can attract "whole life" orders.
Mrs Angiolini said: "Despite a general decrease in crime, violent crime remains a persistent problem in too many communities in Scotland."
And she called on particular guidance to be given to judges dealing with violent crimes involving knives and swords, to reflect statistics which indicated that just under half of the killings in Scotland were "committed by individuals using sharply pointed weapons".
In one of the cases brought by the Crown before the appeal court, murderer Robert Kelly had his punishment part of his life sentence reduced from 20 years to 15 years following his guilty plea.
Kelly, 34, strangled loan firm collector Agnes 'Nessa' Mechan, 64, and hid her body under floorboards in the Govanhill area of Glasgow in 2002. The body was only found four years later.
The second murder case in which the Crown is challenging the sentence involves Brian Boyle, 21, and Greig Maddock, 22.
They were ordered to serve minimum terms of 15 and 12 years respectively in 2007 after murdering father-of-two Brian Bowie in Dunfermline, Fife.
The appeal judges are expected to give their ruling on the matter at a later date.