David Bain will need an admission of wrongdoing by police or irrefutable DNA evidence to boost his chances of receiving compensation, says Justice Minister Simon Power.
Mr Power says those are examples that may amount to extraordinary circumstances, which is one of the tests Mr Bain's case must pass before his compensation claim will be considered.
Mr Bain is not eligible to apply for compensation because his acquittal followed a retrial, but the Government has decided to use its discretion and allow him to make a claim.
He was acquitted last year of charges of murdering five family members in 1994.
Getting compensation from the Government for wrongful imprisonment is always a difficult task, but Mr Bain's legal team was told on Tuesday it must pass an even higher bar than most before its claim will be considered.
The case is not strictly eligible for compensation, but the Government has the discretion to let claims go forward if there are extraordinary circumstances.
However, Mr Bain must still prove he did not murder his family members before those additional extraordinary circumstances will be assessed.
If he passes the two-pronged test, the Ministry of Justice will decide if the claim should go further and be assessed by a QC.
Mr Power says process is complex and will take many months.
University of Canterbury law lecturer Chris Gallivan says establishing innocence on the balance of probabilities is in itself is a very high hurdle.