Many borrowers gave up applying for a loan if they did not have a 20 per cent deposit.
House sales in cheaper areas also dropped off.
But Reserve Bank statistics show the tap is being slowly turned on again to people without big deposits.
The amount of new lending to high-LVR borrowers reached 8 per cent last month.
Once exempt cases under the Welcome Home Loans and construction lending were excluded, 6.7 per cent of new lending was to high-LVR borrowers, up from 5.3 per cent in May.
ASB spokesman Shaun Drylie said banks had become more confident in their ability to measure lending and remain below the 10 per cent threshold.
There had also been an overall drop in lending in June, so the high-LVR portion represented a higher percentage. "It's two-fold, there's more confidence from the banks but also a slight drop in overall lending, given the seasonality."
He said ASB was able to approve almost all high-LVR loan applications from existing customers who met its lending criteria, and some new customers.
He said it had taken time for people to realise it was worth applying and that banks were able to help low-deposit buyers.
ANZ said it is encouraging customers to get in touch. Head of mortgages Sarah Berry said banks erred on the side of caution when the regulations were introduced.
"Now there is a better understanding of how the restrictions work, and this has resulted in more inquiries from customers and incrementally more lending from banks, while staying well within the 10 per cent limit."
Westpac said it, too, was open for business.
"In particular we're committed to helping first-home buyers achieve their goal of owning their own home."
Bankers Association chief executive Kirk Hope expected the rate of high-LVR lending could increase further.
The Reserve Bank is expected to ease restrictions near the end of this year, after conceding the reduction in lending has been sharper than expected.
