Robert Turner, 42, was originally ordered to serve at least ten years as part of his life sentence for the murder of Marc Lancashire. But after the Crown challenged the minimum term, judges at the Court of Criminal Appeal in Edinburgh told him he will now be jailed for 13 years before he can seek release.
The delivery driver was twice freed by courts while facing charges of violence before fatally knifing his victim in the heart after a clash at a block of flats in Edinburgh.
He earlier attacked another man with a crossbow in a murder attempt when he was under a previous bail order facing separate charges, including assault.
But he was freed again on bail by a sheriff in Edinburgh before murdering Mr Lancashire, 22.
Lord Osborne, who heard the appeal with Lord Macfadyen and Lord Johnston, said: "We have concluded that the punishment part selected by the presiding judge was unduly lenient.
"We are satisfied that, when account is taken of the seriousness of the murder, combined with the seriousness of the attempted murder, the punishment part of ten years is clearly outwith the range that can reasonably be considered to be appropriate."
Turner was unanimously found guilty of the murder of Mr Lancashire, at Dunsyre House North in Edinburgh's Calder Crescent last May, after a trial at the High Court in the city.
He was also found guilty of attempting to murder John McConnell, 37, by discharging a crossbow bolt at him and striking him with a knife at Broomhouse Medway, in Edinburgh, on 28 September, 2005.
The trial judge, Roger Craik, QC, said in sentencing Turner that he had delivered a single fatal blow to Mr Lancashire but added it was "a very vicious one". He said the killer's intervention in the fatal clash had been unnecessary.
On the day of the murder Mr Lancashire and a friend had been introduced to Turner and another man.
An argument broke out and Mr Lancashire and his acquaintance left but later returned with the other man holding a golf club. Turner's step-son called his father and the fatal knife attack took place.
Mr Lancashire, who was raised in Merseyside, was known as "English Marc" or "Liverpool" and left behind children aged four and two at the time of his death.
The earlier attempted mudrer of Mr McConnell occurred after he clashed with Turner, of Broomhouse Way, Edinburgh, following a wake for his girlfriend's grandmother at a social club.
Turner left but returned armed with a crossbow. Mr McConnell told the trial: "I heard something going past me. I knew something had been fired. It is not everyday somebody tries to shoot you with a crossbow."
He went and fought with Turner but was wounded in the stomach after he was stabbed.
The appeal judges said the sentencing judge should have taken account of the seriousness of both the murder and attempted murder when fixing the punishment part of the life sentence Turner must serve.