The catalyst for the applications is the conviction for perjury of a jailhouse informant in the 1990 trial at which Tamihere was convicted of the murders of Swedish travellers Heidi Paakkonen and Urban Hoglin.
Witness C was today sentenced to eight years and seven months' prison.
When sentencing Witness C, Justice Christian Whata described the perjury as a "brazen assault on the foundation of our criminal justice system".
Gibson said the perjury conviction against Witness C was "immensely important in terms of what happened at the trial".
"It was very persuasive evidence, but it was all a lie. David has told me that he knew he had no chance when he heard [C] give his evidence."
Gibson, who has long acted for Tamihere, said Witness C's evidence had far reaching implications and was a factor in a contentious and damning piece of identification evidence being put to the jury.
Two trampers eventually testified that they saw Tamihere with a blonde woman together at Crosbies Clearing. Trial judge David Tompkins had ruled the evidence inadmissible because it was tainted by unacceptable police practices.
Rather than put Tamihere in an identity parade, police showed the trampers photos of Tamihere including mug shots and suggested they take a look at him when he appeared in court in Thames on charges of stealing the couple's car.
Crown prosecutor David Morris argued the trampers' evidence was supported by one of the jailhouse informants - Witness C whose testimony has now been found to be false.
Witness C claimed that Tamihere had told him he was almost sprung by trampers.
Tompkins countered: "The danger of doubtful evidence being used to support and corroborate doubtful evidence is obvious".
The Crown successfully appealed Tompkins' ruling to the Court of Appeal and the jury heard from the trampers and Witness C.
The head of the police investigation, the late Detective Inspector John Hughes, later appeared at a parole hearing for Witness C.
In 1992 Hughes told this reporter: "We don't make any recommendations [for leniency] in any shape or form but we believe we have a moral obligation to help them by pointing out [to the Parole Board] that they had testified.
"They are taking a huge risk. They have to get up there and be cross-examined. It takes a lot of courage."
Witness C gave graphic evidence about what he claimed Tamihere had told him he had done to the couple. He also claimed that Tamihere had admitted he gave Hoglin's watch to a family member.
The watch was found with Hoglin's remains a year after Tamihere was convicted. A subsequent appeal against conviction was rejected.
Tamihere, who has other violence convictions, including manslaughter, admitted to stealing the Swedes' car but has always denied having met them, or confessing to their murders.
