Police say they would welcome a law change which mirrors an Australian law about the purchase of cellphone SIM cards.
At present in New Zealand, anyone can buy a $5 SIM card for their pre-paid mobile, effectively giving them annonymity and a phone number to text or call someone.
In Australia, the law requires the person's name and address to be recorded before a SIM card is activated - with documentation to support it.
The Police Organised Crime Unit says the majority of its time is spent chasing people behind anonymous pre-paid phone numbers.
Dectective Inspector Paul Berry says criminals know they can buy new phones and numbers relatively cheaply.
He says the Australian model is a pretty good one to work from.
However, the New Zealand government says it isn't looking at a law change.
A spokesperson for Telecommunications Minister Steven Joyce says the issue is yet to be formally raised with the Government by the police or a telecommunication company.