Two Dunedin state integrated schools have admitted breaching their Ministry of Education maximum roll caps.
John McGlashan College and Columba College heads say the anomalies in their school rolls had occurred by mistake, rather than by design.
Ministry sector enablement and support head Katrina Casey said Dunedin had four state integrated schools - Columba, John McGlashan, Kavanagh College and St Hilda's Collegiate School.
The schools, like all state integrated schools, had maximum rolls set as part of their integration agreements between the Crown and the proprietor, she said.
Under the individual agreements, Columba was permitted a maximum roll of 565 pupils, but had exceeded that by 31 pupils; and John McGlashan was permitted a maximum of 500 pupils and had exceeded that by 27.
''This is in breach of the integration agreement, and our expectation is that both boards of trustees will manage the roll back down to within the maximum enrolment limit.
''We have not turned a blind eye to this, and we will continue to be in discussion with both schools over this.''
Ms Casey said state integrated schools only received staffing and operational funding up to the maximum roll number.
''We do not fund integrated schools for any students they enrol beyond the maximum limit.''
John McGlashan principal Neil Garry said the school had found itself in the situation because its retention rates in years 11, 12 and 13 were the highest they had been.
Boys were tending not to move off into employment or other schools as they had in recent years; there had been international pupils who became domestic pupils; and some boarders had become day boys, and the college liked to keep the boarding house full, he said.
The school finds it difficult to meet that target of 500.
''In 2014, we were 15 over initially, but that [roll] just settled to below 500. This year, that settling didn't happen.''
The school was working with its board of trustees and board of proprietors to sort the imbalance, and they hoped it would be rectified by the end of this year, he said.
''There's no extra money, so there's no cunning plan to draw money away. I think to a certain extent we're a victim of our own success because it's a commodity that people want.''
Columba principal Juliette Hayes said the school was also working to address the issue, and the number of excess pupils had already dropped to less than 30.
She said the problem was partly caused when the ministry permitted the school to temporarily increase its roll so it could take pupils from Christchurch following the 2011 earthquake.
The ministry had removed the temporary roll increase, but pupils and families had decided to remain in Dunedin.
''There's a large group of year 11 pupils at the moment, that will be going through.
''What I've done is forecast the next five years, and what the intake at each level needs to be, to be able to sustain the school roll and get it to where it should be.''
''We're aware that we're over. We're working to address it.''
In an anonymous letter sent to the Otago Daily Times, a ''concerned state school educator'' expressed concerns about the two integrated schools operating outside the Education Act and depriving state schools of pupils, and, therefore, resources.
Kaikorai Valley College principal Rick Geerlofs and Otago Girls' High School acting principal Jock Murley agreed.
''In the current environment in Dunedin, where there is pressure on school rolls, we would be concerned that [integrated] schools are taking on more students than they are allocated or eligible to take,'' Mr Geerlofs said.
''Those students could be going to some of those other state secondary schools, where there is some pressure on rolls.''
State integrated schools are former private schools that were integrated into the state education system under the Private Schools Conditional Integration Act 1975.
They were established in response to the near-collapse of the private Catholic school system.
There are now about 330 state-integrated schools in New Zealand, educating about 87,500 pupils, or 11.5% of New Zealand's pupil population.