Police Assistant Commissioner Richard Chambers says waiting times at Auckland checkpoints are down and more motorists are turning up with the documents needed.
Some of those travelling are reporting that things have improved in the past week, others say it's still a shambles.
Chambers said average waiting times at the southern checkpoints were down to 30 minutes yesterday, and five minutes in at the northern side.
He told Morning Report 86,000 vehicles had turned up at Auckland checkpoints since midday Wednesday last week.
Of these 4800 have been turned back.
Earlier this week truck drivers with perishable goods on board had reported being held up for hours as they negotiated the city's border controls, prompting Nick Leggett from the Road Transport Forum to call for clarity on the documents needed and better processing of truck drivers who already had an exemption.
Chambers said two of the southern checkpoints have had a "tremendous volume" of traffic, with more than 20,000 vehicles passing through each, which was why they've made changes, he said.
The dedicated line for freight trucks in the south "seems to be working very well". There had also been big improvement in motorists turning up with the documentation required, which helped speed up the process, he said.
"We've applied a commonsense approach and I think everyone realises it's not an easy process when you're shutting down New Zealand's biggest city in this way.
"As time goes on, people have had more time to understand what those expectations are and they're rising to those expectations as well."
Border restrictions are preventing residents in two townships in northern Waikato from legally getting to a supermarket or dairy. Otaua and Aka Aka are flanked by the Waikato River in the south and Auckland's border in the north, and don't have food retailers. Some residents haven't bought food in a week - living off what they have, or their land - while others are breaking the law to do so.
Farmers with properties either side of Auckland's southern border are frustrated they haven't been able to check stock or get essential supplies because of the alert level 3 lockdown.
Foodstuffs says it is working with government to find ways to serve customers who live just outside the Auckland border and usually shop within the level 3 zone. The border closures have affected some of the staff working at the company's New World, Pak'n'Save and Four Square stores, along with the supermarkets' ability to do online deliveries.
North Island chief executive Chris Quin told First Up the company was working with the communities to see if there is anything they can do to help without breaching any health orders.
Quin said the company was also trying to get itself included in exemptions so staff members can travel to work and shelves can be replenished.
The Ministry of Health said yesterday it had so far received more than 5000 applications for travel exemptions. About 700 had been granted and 160 declined.
Director general of health Dr Ashley Bloomfield said a team was working as fast as possible to process them.