The experience of my friends and colleagues is that NZ will entertain comps from QF especially if your travel is either trans-tasman or to LAX. They weren’t too fussy on fare class (i.e. back of the bus on discount fares was OK) just wanted to see a reasonable amount of business that may come their way. The Airpoints people weren’t too cluey as to what a comp was – but a well set out letter, with the request and some evidence of flights on QF received a fairly prompt (and indeed favourable) reply.

A number of years ago – I did some temping for JAL in their Sydney office and spent a couple of weeks doing data entry for the FF. One of the envelopes I opened was a request for a comp from ANA (at this time NH were serving SYD). I passed it on to the head of the department who in turn sent a message to head office. HQ came back and authorized the comp … The rest of the grunts doing the legwork in the department weren’t too clever on how things operated but the team leader later told me that she was authorized to match status for very frequent flyers and was to send a message to HQ for anything else. She said that she always requested it via HQ regardless of what sort of comp request it was (just to be safe I think – the whole office was paranoid about making a decision that was later frowned upon) but had yet to deny any request. This was however, a number of years ago so needs to be taken as being somewhat dated.