[MotherBear]

Tom, from the same link above, here's a list of what's temporarily exempt from being taxed.

Types of foreign income which are temporarily exempt from tax in New Zealand:

Controlled foreign company income that is attributed under New Zealand's Controlled Foreign Company (CFC) rules
Foreign investment fund income that is attributed under New Zealand's Foreign Investment Fund (FIF) rules (including foreign superannuation)
Non-resident withholding tax (for example on foreign mortgages)
Approved issuer levy (for example on foreign mortgages)
Income arising from the exercise of foreign employee share options
Accrual income (from foreign financial arrangements)
Income from foreign trusts
Rental income derived offshore
Foreign dividends
Foreign interest
Royalties derived offshore
Income from employment performed overseas before coming to New Zealand, such as bonus payments
Gains on sale of property derived offshore (held on revenue account)
Offshore business income (that is not related to the performance of services).