When Carroll realised Tucker had died, he and an associate drove out to Lake Ellesmere, wrapped Tucker's body in carpet and set it on fire.
The charred corpse was found the next day by a group of fishermen.
Carroll was sentenced by Justice Nicholas Davidson to life imprisonment with a minimum non-parole period of 17 years.
At a Court of Appeal hearing in Dunedin yesterday, defence counsel Anselm Williams argued Carroll's actions did not warrant an elevated prison term as dictated by section 104 of the Sentencing Act.
That legislation dictates that murders committed with a "high level of brutality, cruelty, depravity, or callousness" must be reflected by a minimum jail term of at least 17 years.
While Williams accepted there was a degree of brutality and callousness to Carroll's behaviour, he said it was not among the worst murders seen by the courts.
He noted Justice Davidson found the killing "reckless rather than intentional".
During his submissions he accepted the victim was not the person Carroll intended to kill, over a perceived wrongdoing to a third party.
Justice Forrie Miller questioned whether such vigilantism required a lengthy sentence to satisfy the principles of denunciation and deterrence.
Crown prosecutor Mark Lillico said Carroll exhibited extreme callousness at all three phases of the murder - before, during and after.
"It's not a spur-of-the-moment thing," he said, referencing the premeditation in selecting the weapon.
Lillico also noted evidence that the beating lasted some time and involved Carroll "coolly" telling the victim to stop resisting.
He described what was done to Tucker post-death as an "indignity".
Justice Stephen Kos, Justice Miller and Justice Christine French reserved their decision.
