Two men, whose convictions for the 1987 Red Fox Tavern murder were overturned by the Supreme Court last month, are seeking costs from the Crown.

Publican Chris Bush was fatally shot at the Maramarua pub and two balaclava-clad offenders fled with more $30,000.

The case went unsolved for almost 30 years before James Wilson and Mark Hoggart were charged and subsequently convicted in 2021.

Last month, the Supreme Court acquitted the pair after deliberating two years, finding there was no reliable evidence to prove they were at the scene of the crime.

Lawyers for Wilson and Hoggart had earlier failed in their bid to overturn their convictions at the Court of Appeal.

On Wednesday morning, the case was called in an administrative hearing at the High Court in Auckland.

Justice Mathew Downs said he'll defer the next court date until the shape of application is better known.