Clayton Weatherston has had his application to appeal his murder conviction rejected.
The 35-year-old is serving a life sentence with a minimum non-parole period of 18 years for the 2008 murder of his former girlfriend Sophie Elliott.
Weatherston had sought leave in the Supreme Court to appeal the Court of Appeal's earlier dismissal of his appeal.
In its ruling today, the Supreme Court said two matters had been raised in the appeal.
The first was whether a television interview with a Law Commissioner during Weatherston's trial affected the fairness of the trial.
The Supreme Court said while it was unfortunate that the Commissioner chose to go on television on the subject of the provocation defence while a well-publicised trial was underway in which such a defence was being advanced, he was not commenting on Weatherston's case nor on his particular use of the defence.
"His statement was made on a channel with a very small audience and did not achieve much prominence.
"... If television coverage caused adverse sentiment in the community towards Mr Weatherston, that was because of how he conducted himself at the trial.
"... Any reaction to Mr Weatherston's unusual conduct was generated by Mr Weatherston himself."
The second matter raised was whether the prosecution should have obtained leave from the trial Judge before challenging Mr Weatherston's accuracy by cross-examining him on what he'd said about events prior to the murder.
"... This argument likewise has no prospect of success. The Court of Appeal correctly interpreted and applied the Act ...
"In any event, leave would surely have been granted.
"The Crown had good reason to want to challenge what the applicant had said about the incidents in question and was obliged ... to do so by cross-examination.
"The matters involved were significant and relevant and the Crown needed to be able to contradict him on them."
The Supreme Court said no arguable matter of public or general importance was raised and there is no appearance that there may have been a substantial miscarriage of justice.