David Bain's key supporter, Joe Karam, says he is pleased previously suppressed evidence against Mr Bain has now been heard.
The Supreme Court lifted suppression on part of Mr Bain's 111 phone call, which contained audible breath sounds that the Crown claimed were Mr Bain uttering the words "I shot the prick".
The jury did not hear that segment of the tape.
Mr Karam believes releasing the audio removes speculation about what was said.
Linguistic experts disagreed about whether the sounds were even words at all, he said.
In addition, the Court of Appeal lifted suppression on an allegation that Mr Bain was planning a sexual attack on a female jogger and had intended to use his newspaper run as an alibi.
Neither the tape segment nor the rape allegation was permitted to go before the jury in his retrial after it was challenged by the defence team.
But the two courts on Thursday ruled that the information could now be made public.
Mr Karam said the suppressed part of the 111 call was a joke and the words "I shot the prick" did not exist. There was no confession, there were no words and he refuted any suggestion they existed.
He also said the suggestion Mr Bain was planning a sexual attack on a jogger was a fantasy of the person who offered the alleged evidence.
The Court of Appeal judgment relates to information from two former schoolmates of Mr Bain.
One of them, Mark Buckley, told a pre-trial hearing that Mr Bain had discussed a rape with him in 1989 or 1990, and had detailed in a notebook how to use his paper run as an alibi. It involved him delivering some newspapers earlier than normal and ensuring he was seen by other clients at the normal time.
But no rape took place and the information was ruled inadmissible in the retrial.
Crown Law denial
Meanwhile, Crown Law categorically denies it offered a plea bargain in Mr Bain's retrial, despite Mr Karam saying it did.
Mr Karam told a media conference in Auckland on Thursday afternoon that Crown prosecutor Kieran Raftery offered chief defence lawyer Michael Reed, QC, an informal plea bargain - an offer he rejected.
Crown Law would not comment further.
Last Friday, a High Court jury in Christchurch found Mr Bain not guilty of the murder of five members of his family.
Thursday's court rulings do not affect Mr Bain's acquittal.