However, Chief Justice Dame Sian Elias and Justices Sir Peter Blanchard and Sir William Young rejected that argument in their decision released yesterday. They said the court had to strike a balance between open justice and the interests of whoever was seeking suppression but it was not a factor in respect to Mr Hart.
"The likely particular impact of publicity on that party will always be relevant, but it is untenable to suggest that professional people of high public profile, such as the applicant, have anything approaching a presumptive entitlement to suppression."
Mr Hart has represented some notorious criminals, including Antonie Dixon, who attacked two women with a samurai sword and shot a man dead in 2003. Another was Joseph Martin Reekers, who later admitted killing Marie Jamieson and dumping her body behind a West Auckland factory.
Mr Hart has maintained a high media profile as a commentator on legal issues.
His requests for suppression had been considered by the tribunal, a High Court judge and reviewed by the Court of Appeal, the Supreme Court trio noted.
"We see no arguable error in the approach taken in the Court of Appeal [and] it follows the application for leave to appeal must be dismissed."
Mr Hart could not be contacted last night.
The hearing into the charges was supposed to be in November but before it could get under way, much of the time allocated was used for legal arguments.