More than 800 signatures have been collected in a petition opposing compensation for David Bain, who was acquitted of the murders of five family members in a retrial this year.
The petition is being organised by supporters of David Bain's father, Robin Bain.
A spokesperson for the group, Kent Parker, says there is growing public opposition to the idea of Mr Bain being awarded compensation for his years in jail, reflected in the number of hits on the group's website and signatures on its petition.
He says the Justice for Robin Bain Group believes the trial jury was unduly influenced by the promotion of Mr Bain's innocence by his supporter, Joe Karam.
Mr Parker says a review is needed of issues including how much promotion should be allowed by a defendant's spokesperson, and whether a jury should be expected to deal with the evidence of expert witnesses without professional guidance.
The group is also questioning whether there should be a time limit on trials, suggesting expecting a jury to concentrate for 58 days - as was the case in Mr Bain's retrial - is unreasonable. It is also questioning whether the amount of legal aid provided should be limited.
The group is aiming to collect 10,000 signatures on its petition to Justice Minister Simon Power.