With more people than ever wanting to donate their bodies to science, Otago University's medical school has had to introduce a quota system to manage numbers.
Letters have been sent out to registered donors, explaining that the number of cadavers accepted each year needs to be capped.
Kathryn McClea, bequests co-ordinator at the Otago's School of Medical Sciences, said today the university had to restrict the number of bodies it took, as it could only store 80 at a time.
The university was now close to filling its quota for the year, and had 1800 people on its books.
"We've realised that this is going to be an ongoing situation."
The university has explained to would-be donors that it has introduced an annual quota, and when that number is reached it is not able to accept any more bodies for the rest of the calendar year.
Funeral directors would be notified of the quota being filled.
The details of those wanting to donate would remain on the database for subsequent years and quotas would reopen on January 1 each year.
Ms McClea said the matter was sensitive and was difficult to manage as there was no way of predicting how many bequestees would die in a given year.
As the university took care of transport and cremation of body parts, Ms McClea urged those who had registered with the university to ensure they had alternative funeral arrangements in place in case their bodies were unable to be accepted.
The university's bequest programme has been increasing in popularity since 2000, with an average of 200 people registering a year.
Ms McClea attributed it to the fact that people were more aware that donating their bodies was an option, and that it was a subject that was talked about more openly now than in the past.
Auckland University's bequests co-ordinator Valerie McMurtry said its medical school had not implemented a quota system but judged whether it could accept bodies on a case-by-case basis.
The number of bodies it accepted fluctuated considerably for a number of reasons, including cause of death, time elapsed from death, distance and transportation time involved, and family reluctance to go through with the bequest.
However, she said she had "filing cabinets full of registrations".
New Zealand's situation bucks an international trend in which the training of medical students is said to be jeopardised by the shortage of bodies to work with before they graduate.
The Royal College of Surgeons in Britain has said it faces a 30 percent shortfall, with particular problems in London.