Bracken's lawyer Warren Pyke submitted in the appeal, the admission of propensity evidence needed to be reconsidered and said the judge permitted cross-examination about irrelevant, speculative, emotive and prejudicial claims about Bracken's state of mind.
Mr Pyke submitted a miscarriage of justice had occurred and that Bracken sought a change reduction of sentence, to a minimum term of 19 years.
In a written decision the Court of Appeal dismissed both the appeal against conviction and the sentence.
"We are satisfied that the appellant had a fair trial. The conviction appeal is dismissed."
They further concluded that the end sentence of 21 years was not excessive, and the sentence appeal was also dismissed.
During the trial the jury heard how 30-year-old Mr Davis was kidnapped and "hog tied'' before being driven into remote bush where he was murdered with a thistle grubber.
Mr Davis died in bush off the Wairakau Track on February 25, 2011 - a day after he was kidnapped, had his limbs bound together, and was kept overnight in a woolshed on a farm belonging to Mr Dangen in Salvation Rd, near Kaeo.
During the trial a video interview with police, hours after Mr Davis' body was found, was played and Mr Dangen described how Bracken had emerged from the bush "dripping with blood" and smiling then stripped to his underwear and later burned the clothing.
Justice Edwin Wylie noted during sentencing Bracken had taunted Mr Davis' family by singing and whistling Candle in the Wind when he entered and left the courtroom during the trial, continuing even after being asked to stop.
"It was calculated and vicious. It was, in effect, an execution," Justice Wylie said of Mr Davis' death.
The judge said Bracken was "dangerous and evil".
Forensic evidence given during the trial showed seven lacerations around Mr Davis' neck were between 3cm and 7cm long and were likely to have been made by a thistle grubber. The cuts to the neck included one which severed the carotid artery and another that sliced the esophagus and fractured the fourth vertebrae in Mr Davis' neck.