The overwhelming majority of those surveyed by the Privacy Commissioner want the agency to be given the power to stop organisations mis-handling their personal information.
At present, the Privacy Commissioner has the power only to negotiate with organisations or threaten public exposure if they breach people's privacy.
The survey released by the commission on Wednesday shows 97% of those questioned would support the agency having increased powers.
Natasha Fuller made a complaint to the Commissioner in 2009 when Social Development Minister Paula Bennett made public details of benefits Ms Fuller was receiving.
The complaint was upheld but Ms Fuller says the process has taken years and changed nothing.
Commissioner Marie Shroff says changes suggested by the Law Commission to allow her to stop privacy breaches or audit information-handling practices would speed up the complaints process.
The survey carried out by research company UMR, has a margin of error of plus or minus 3.6%.