They pay up to NZ$4000 for this - and spend up to a fortnight recovering.
The revelation come from a surgeon who has researched the shape of the ideal male nipple.
Jeyaram Srinivasan, of the Royal Preston Hospital, asked 62 volunteers to study topless photos of 100 men and say which had the most desirable nipples.
Some of the models were ordinary males who worked in the hospital, others were body-conscious gym goers.
Both sexes plumped for symmetrical nipples that were small, flat and slightly darker than the surrounding skin.
The ideal nipple is also round or almond-shaped, the British Association of Aesthetic Plastic Surgeons annual conference heard.
In case you are wondering, David Beckham, apparently, has perfect almond-shaped nipples.
Dr Srinivasan's study also showed that women are more put off than men by nipples that protrude.
The surgeon, who does private as well as NHS work, does around 40 nipple reductions a year.
Most of these are in men whose nipples seem to large after extreme weight loss or after surgery to remove their 'man boobs'.
But some are in men who are simply anxious that their nipples are too big.
These men are often body builders who have compared their chest to other men in the gym.
Dr Srinivasan said: "For many years, cosmetic surgery was associated with women and men wouldn't even talk about it. They thought it was too vain.
"But now, men say: 'If I can have something to make me look better and I can afford it, I will do it.'
"The view has changed."
Those can't afford the operation or are squeamish about the 45-mintue procedure have another option.
The study showed that a sculpted chest can often more than make up for nasty nipples.
Dr Srinivasan said: "A well-toned torso will make people accept a nipple that is less than ideal.
"They are distracted by something more important to look at."
- Daily Mail