The first notices issued last year were to users who had allegedly illegally downloaded songs by R&B star Rihanna and pop star Lady Gaga.
Movie studios are not believed to have sent out any warning notices.
The chief executive of internet provider service Orcon Scott Bartlett said he expected downloading would drop off slightly when it became known that somebody had received their final notice.
"How far and how fast it bounces back will depend on the perceived danger of continuing to illegally download copyrighted material," Mr Bartlett said yesterday.
Although the volume of international peer-to-peer traffic over Orcon's network had dropped by about 10 per cent after the new law came into effect in September, it had now climbed back up.
Peer-to-peer software forms a connection between many computers and lets users search for and download files stored on any of them.
The software is a popular way for web pirates to illegally share copyrighted material, although it also has a large number of legitimate users.
Industry insiders say internet pirates using peer-to-peer software are caught out by independent companies who find illegal downloaders by joining users who log on to sites such as Pirate Bay to share files.
The spy computer records the downloader's internet Protocol (IP) address - which identifies the computer being used - and the section of copyright file received.
The detection company then gives the information to the copyright holder, which can send an infringement notice to the downloader via their internet company.
But Telecommunications User Association chief executive Paul Brislen says many people downloading music and movies have switched to more covert and secure means.
"[Researchers have seen] a 25 or even 30 per cent increase in the number of secure VPNs [virtual private networks] that are set up. What that says to me is that anyone who knows anything about this is simply tunnelling to the US and UK and carrying on regardless," Mr Brislen said.
VPNs mask a user's identity and make it difficult to track IP addresses.
WHAT HAPPENS
* Three warning letters
* Tribunal hearing
* $15,000 fine (maximum)