ANZ cut its servicing sensitivity rate from 7.25% to 6.9% in late August. In a note to advisers, the bank said it had listened to "survey feedback".
ANZ has also separated its loan affordability calculator, making it a standalone form.
The change comes after the Reserve Bank cut the OCR by 0.5% in August, prompting home loan rates to fall to record lows.
Regulatory changes have also made it easier for banks to ease servicing rates. Australian regulator APRA abolished its minimum 7% testing rate for banks in August.
An ANZ spokeswoman said: "We review our servicing sensitivity rate (SSR) on a regular basis. We reduced our SSR following August’s Official Cash Rate (OCR), cut taking into account falling interest rates, the long-term OCR outlook and recent APRA requirements."
Meanwhile, ASB has changed the interest rate used to determine loan servicing of uncommitted monthly income from 7.7% to 7.2%. The bank said it had "listened to feedback" from advisers.
Stephen Wilton, an adviser at The Advice Group, says the changes have had a slight impact on pass rates for borrowers, but says allowances still make it tight for borrowers.
"For the most part, standard mum, dad, two kids deals are pretty much of a muchness over all banks ... It does seem like a lot of deals are looking much better in terms of a pass rate, although when it comes to investors (calculated on P & I), there's still a bit of a battle."
Glen McLeod of Edge Mortgages said bank serviceability rates still hovered around the 7% mark. He doubts whether serviceability rates will fall much further in the near term: "If you look where we are, that's almost double [compared to current home loan rates]. If you look at the Responsible Lending Code, do banks have much choice?"