It has taken 30 years but men convicted of homosexual acts could get the right to apply for a pardon next year.
1 NEWS has confirmed the Cabinet will consider a plan to clear convictions before the 1986 law change that meant homosexuality was no longer illegal.
Thirty years after homosexual law reform, historical convictions for consensual sex between men are still a thorn in the side of the gay community and gay rights campaigners like Des Smith and John Jolliff want these convictions reversed.
"It seems to me quite immoral and unjust for that criminal record to be retained for them. It's affected their life for a long time and there should be an apology from Government," said Mr Jolliff.
1 NEWS has learned Justice Minister Amy Adams has asked officials to work on a solution.
The 1961 Crimes Act outlawed male sex, whether it was consensual or not.
The fight to change that met fierce resistance, and although reform won, convictions were never erased.
Justice Ministry figures show that between 1980 and 1986 there were 879 convictions.
Last year campaigners took a petition to Parliament.
Many of the public would like to see this happen and it should happen- John Jolliff, gay rights campaigner
"Pardoning men who were convicted of homosexuality is a great step towards improving the justice in our society," said Wiremu Demchick, gay rights campaigner.
But there won't be a blanket pardon. Men or their families will have to apply for one. That's because some convictions were for sex with a minor, which is still a crime.
"I believe many of the public would like to see this happen and it should happen... just on the grounds of natural justice people should not have this shadow over them for the rest of their lives," Mr Jolliff said.
In a statement to 1 NEWS, Ms Adams said it was a "complex and unprecedented issue".
Des Smith said: "Just put yourself in the shoes of that person who has been prosecuted and persecuted. And just think about it and maybe you'll open up your mind."
And the Government is promising to do just that.