Low-deposit lending had been about a quarter of the market for many banks.
Bruce McLachlan, chief executive of the Co-operative Bank, said it was hard for banks to work out how much they could lend.
They could estimate at the start of the month how much money should be made available to low-deposit borrowers but it would be affected by how much lending was done in total.
His bank had a target of 8 per cent low-deposit loans but had come in below that each month so far as demand from borrowers with more equity was higher than expected.
In January, the co-operative had lent a little over 6 per cent of its new loans to low-deposit borrowers.
ASB chief executive Barbara Chapman said the sharp reduction in lending had been because banks needed time to get their systems right to deal with the rules.
But she said now it was confident it had some headroom and could remain within the 10 per cent limit, ASB would be able to do more lending over the coming months.
Westpac chief economist Dominick Stephens said that was the experience of most of the banks, and could mean that the sharpest impact of the rules had passed.
He said rising interest rates would have more of an impact on house prices than the lending restrictions.
A Herald on Sunday/Key Research poll asked what people thought of the rules. Two-thirds said the restrictions would not have any impact on house price growth.
More than half said it would make it easier for overseas buyers to purchase properties in New Zealand, and 48 per cent said they would make life easier for investors.
But 92 per cent said it would be harder for first-home buyers to get into their own homes. And 85 per cent said it would make first-time buyers more likely to rely on loans from their parents or finance companies.
Property expert Olly Newland was not surprised the restrictions were not popular. He said a better solution would be to have a two-tier interest rate system, where investors paid a higher rate. "That would be far more sensible and fair."
At present, many banks charge people with a small deposit a higher rate of interest.
Newland said there was already increasing pressure on the rental property market as people were stuck as tenants longer while they saved for a deposit. But he said the restrictions would likely have little impact on prices, which would continue to rise over the year, at least until the election.
Real Estate Institute chief executive Helen O'Sullivan said the restrictions had prompted more of a decline in turnover in the cheapest price brackets and in the regions rather than in Auckland and Christchurch.