If you're refixing your home loan, it's worth pushing for a rate discount, brokers say - because there are often "secret" specials and cash back incentives available.
ANZ surprised the market on Tuesday with a 5.59 percent one-year fixed term made available on its app.
It was still advertising a one-year fix at 6.19 percent.
The cheaper rate was available to borrowers with at least 20 percent equity.
Mortgage adviser Karen Tatterson, of Loan Market, said she had not seen other banks match the ANZ rate yet but ASB had reduced a number of its rates by 10 basis points on Wednesday morning - and its one-year rate by 16.
"ANZ does tend to offer a slightly lower than carded rate if we push for this but it is dependent on the swap rate and what the market expectations are."
She said the rates offered to refixing customers online and via the app were often the best rates available, but it was worth checking.
"I always recommend that I chat with the clients once they have the online rates to confirm whether these are the best rates or not.
"If so, then we are encouraged by the banks to get them to lock in online. If the rates, in my opinion, are not competitive, then we will go to the bank on their behalf and seek better rates."
Another mortgage broker, Jeremy Andrews of Key Mortgages, said ANZ seemed to be backing up its view that the OCR would drop sharply.
He said he had heard from bank staff that refixes were "unusually quiet", which could indicate that people were holding off and hoping for big drops in rates before locking one in.
"We're bracing ourselves to get busy here."
He said ANZ was the main bank still using higher advertised rates alongside notably lower specials but he would always negotiate for the best discount possible.
Tatterson and Andrews said banks were offering cashback deals to many borrowers.
Tatterson said $5000 would be a common amount for first-home buyers to be offered, or 0.8 percent or 0.9 percent of the loan amount.
But she said, at the moment, borrowers were more concerned about rates.
Andrews said he was seeing more cashback for those with less than 20 percent deposit than had previously been common and more generous offers for people with more than 30 percent equity.
"There are also different caps with different banks and we've got over $15,000 cashback recently for a client with a larger mortgage."