The man who killed British backpacker Grace Millane has lost his bid to appeal his conviction for her murder.
Kempson was handed a life sentence with minimum non-parole period of 17 years after being found guilty in a highly publicised trial in 2019 for Millane's murder.
The 28-year-old strangled Millane on the eve of her 22nd birthday in his CityLife apartment in Auckland's CBD in December 2018.
His interim name suppression lapsed late last year, after which it was revealed he had also been found guilty on sexual violation offences relating to two other women.
The Supreme Court today dismissed Kempson's application for leave to appeal his conviction. It means he has exhausted all his options for avoiding jail time for the murder.
The Court of Appeal had already dismissed his appeal against conviction and sentence.
The Supreme Court judgement said it was common ground that Kempson killed Millane by applying pressure to her neck.
But the defence had argued that Millane had consented to this action, while denying there was murderous intent.
"The conclusion of both courts is that consent does not, at least in the circumstances of this case, provide a defence to the intentional infliction of bodily injury known to be likely to result in death," the ruling read.
"There is insufficient doubt as to that conclusion to warrant leave being granted. This is because it is difficult to see how a court could responsibly hold that consent is a defence to violence carried out with murderous intent.
"By their verdict, the jury showed that they were sure that if the applicant did not intend to kill the deceased, he at least intended to inflict bodily injury which he knew was likely to result in death," the decision said.
"The most that could be taken from the applicant's account is that Ms Millane may have consented to the application of manual pressure to her neck...
"There is nothing in what the applicant told the police to suggest that she consented (or he believed she consented) to the infliction of bodily injury of a kind likely to kill her.
"For these reasons, albeit slightly differently expressed, the Court of Appeal was of the view the argument failed 'as a matter of fact'."
The Supreme Court saw "no apparent error in this conclusion" and dismissed the application.