The teenager who abducted, raped and murdered Alesha MacPhail is appealing against the 27-year minimum sentence handed down to him.
Aaron Campbell was 16 when he was sentenced to life for killing the six-year-old on the Isle of Bute.
His counsel, Brian McConnachie QC, told the Court of Criminal Appeal in Edinburgh that the 27-year term was excessive in light of his age.
Three judges will give their ruling at a later date.
Lady Dorrian, sitting alongside Lord Menzies and Lord Drummond Young, said: "This is a matter that requires proper consideration and reflection over time and accordingly we propose to take time to consider our decision which will be issued in due course."
Campbell, now 17, followed proceedings in the court via a live TV link from Polmont young offenders' institution in Stirlingshire.
He is serving one of the longest terms of detention ever imposed on a juvenile offender in Scotland.
His counsel Mr McConnachie told the three judges at the start of the appeal: "It was clearly an appalling and heinous crime.
"The outcome of this appeal will not determine when, or indeed if, the appellant is allowed release."
Mr McConnachie said that, ultimately, the question of whether Campbell was ever released would lie with the parole board if they concluded it was safe to do so.
He added: "I accept, indeed as does the appellant, that day may never come."
But Mr McConnachie added: "Due to the appellant's age the punishment part selected was excessive and as a result amounted to a miscarriage of justice."
He said that Campbell was a child at the time he committed the offence and the courts have previously recognised that special considerations are taken into account in sentencing children, including immaturity and rehabilitation.
Mr McConnachie said that reports prepared on Campbell were "frankly incredibly negative, pessimistic and understandably so".
But he said that to wait until Campbell was 43 before he became eligible to apply for parole was "an extraordinary length of time" which did not allow for maturation, development of responsibility and growth of personality.
He referred appeal judges to the case of murderer Luke Mitchell, who was 15 when he killed his 14-year-old girlfriend Jodi Jones in Easthouses, Midlothian, in 2003.
Appeal judges rejected Mitchell's challenge against a 20-year minimum term by a majority, with the then Lord Justice Clerk, Lord Gill, dissenting and stating that the punishment part was excessive due to his age.
Mr McConnachie said: "In my submission, the remarks of the Lord Justice Clerk are remarks which apply to this case."
Alesha, from Airdrie, North Lanarkshire, was only a few days into a family holiday in Rothesay when Campbell took her from her bed in the middle of the night on 2 July last year.
The child's body was found in the grounds of a former hotel the following morning.
A post-mortem examination later revealed she had suffered 117 injuries.
During his nine-day trial in February, Campbell lodged a special defence naming the 18-year-old girlfriend of Alesha's father as the killer.
He also took the stand and told the jury his DNA must have been planted at the crime scene.
However, before sentencing it emerged that he had confessed to the killing.