The two young people disappeared during New Year's Eve celebrations in Marlborough Sounds in 1998. Scott Watson has long claimed his innocence and is set to launch his latest appeal in June next year.
A Court of Appeal hearing on Thursday considered whether his legal team would be allowed to include two expert reports on DNA evidence in his appeal.
Crown lawyer Madeleine Laracy argued lawyers for Watson needed to explain how the evidence was fresh, or if it was not new, why it should be included.
"The way the appellant would be expected to deal with that would be to say well this is what was known at trial," she said.
"This is what we know from the record and from the other material we have about how these matters were explored in preparation for trial, this is what's different now, and that difference is what allows the court to assess well, is it really cogent? Has it really made a difference? And, is it in the interests of justice that we revisit these issues?"
The case was referred back to the Court of Appeal in 2020 by then governor-general Dame Patsy Reddy, after reports from a forensic scientist called into question the reliability of hairs found on a blanket on Watson's yacht, thought to belong to Hope.
"There is no indication so far of what the specific issues are in terms of routes to contamination that are going to be pursued.
"In that five days, where there's going to be at least two days of submissions, we're going to get through 11, plus maybe two more, expert witnesses, plus anyone called by the Crown in response."
However, Watson's lawyer Nick Chisnall argued the matter would be better decided at the full hearing next year, noting the case had been referred back by the governor-general because of concerns about the evidence
"As the reference explicitly states, evidence has become available since the trial and appeal against conviction that may raise doubts about the reliability of an important aspect of the prosecution case, which is the hairs," he said.
"Ultimately what matters is putting [the reports] in context. Placing that evidence alongside other evidence and looking at what happened at trial, and then determining whether that evidence would have resulted in more favourable verdicts had it been before the jury."
Chisnall described the reports as "modest evidence" and the grounds for the appeal were already confirmed.
The Crown was overblowing the issue, he said, by suggesting they would negatively affect the proceedings if they were not ruled admissible by the court before the appeal.
The justices reserved their decision.
