Cameron Logan, 23, died in the blaze at his family home in Milngavie, East Dunbartonshire, in the early hours of January 1.
Paige Killer's Written Appeal Decision
Judges are to issue a written decision on an appeal to reduce the 27-year sentence of Paige Doherty's killer.
John Leathem, 32, stabbed the defenceless teenager 61 times and inflicted a total of more than 140 injuries when she stopped for a breakfast roll at his Delicious Deli in Clydebank, West Dunbartonshire, on March 19.
Despite claims he was in "a panic'', he cleaned up his crime and dumped the 15-year-old's body in bushes near Great Western Road two days later.
The businessman, who admitted Paige's murder, was given a mandatory life sentence at the High Court in Glasgow in October and ordered to spend at least 27 years behind bars.
He launched an appeal against the minimum jail term later that month and his case was heard by senior judges at the Appeal Court in Edinburgh on Friday.
Leathem appeared by video link from prison as his lawyer Iain Duguid QC addressed Lady Dorrian, Lord Bracadale and Lord Turnbull.
Paige's mother Pamela Munro was joined by family and friends in the court to listen to the appeal.
Mr Duguid said: "Nothing I say is intended to diminish the seriousness of the offence ... it is simply a matter of law.''
He said Leathem's sentence - which included six years for an attempt to defeat the ends of justice - was "excessive'' and ``inconsistent with comparable cases''.
The lawyer said the murderer had no previous record of offending and had shown ``genuine remorse''.
Mr Duguid said the punishment part of Leathem's sentence for murder was higher than other child murder cases and ``represents a significant increase in the tariff'' for such offences.
The lawyer also compared the sentence handed down to Alexander Pacteau for the murder of Irish student Karen Buckley last year.
Pacteau was sentenced to 23 years for the killing and trying to dispose of the body in a barrel of chemicals.
Mr Duguid said his client's actions were "no comparison'' and suggested Leathem had said he dumped Paige's body deliberately in a spot where it would quickly be found.
The defence lawyer said: "He (Leathem) never tried to dismember or destroy this girl's body.
"He took it to a deposition site that, he indicated, he thought it would quickly be discovered.
"It is no comparison to the actions of Pacteau.''
Mr Duguid also referenced sentences and reductions handed down in murder cases including Linda Spence, who was abducted and tortured, baby Maddison Horn killed by her mother's boyfriend, and three members of the Sharkey family killed in a fire attack at their home in Helensburgh.
Advocate Depute Iain McSporran spoke briefly at the hearing to address the issue of when Leathem first entered a plea.
After the submission, Lady Dorrian said: "We should take time to make our decision, particularly as it may have consequences for other cases.''
The decision will be issued in writing at a later date.
Paige's family left court without comment but a petition opposing any reduction in Leathem's jail term has been signed by thousands of people.
Ms Munro, who has three other children, recently told the Sunday Mail: "Even if he got out at 59, he'd still have a life, so 27 years isn't long enough. He's totally deluded. This appeal is cruel.
"With the appeal being on December 23, there is no way that our first Christmas without Paige can be a normal one - as much as we might try to make it that way for the kids.''
Ross Monaghan, 35, was shot near St George's Primary School in the Penilee area of Glasgow.
Support staff working in Scotland's schools are feeling exhausted, undervalued and stressed, according to a trade union study.
Police investigating the death of a man in South Lanarkshire have made an arrest.
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