Barclays has reported seeing the first drop-off in payment protection insurance complaints in three years during the first half of 2013.
However, the bank is also accepting it is in the wrong in a higher proportion of cases, upholding nearly seven in 10 PPI-related complaints in consumers' favour, compared with closer to six in 10 a year ago.
Some 290,525 insurance-related complaints were made to Barclays Group in the first six months of this year, of which the vast majority were about PPI.
This marked a 1% drop from a peak of almost 295,000 complaints recorded in the last six months of 2012, although the latest figure is still 2% higher compared with the same period a year ago.
A Barclays spokesman said that the monthly flow of PPI-related complaints the bank is seeing has been starting to decline recently, although the situation is being kept "constantly under review".
Explaining the increase in the number of claims which are being upheld, he said the bank is getting less "spurious" complaints made by claims management firms. It has also been proactively mailing those customers it believes may have a legitimate complaint, inviting them to come forward. The bank added an extra £1.35 billion to its provision for PPI payouts last month.
PPI mis-selling has surged to become the biggest financial scandal that the ombudsman service has ever seen. More than £10 billion has already been paid out by the industry to compensate victims, many of whom had not even realised that they had the insurance.
A spokeswoman for the Financial Ombudsman Service (FOS), which steps in resolve financial complaints when consumers cannot come to an agreement with their banks, said it has not yet seen any sign itself of PPI complaints tailing off generally.
The spokeswoman said: "We have heard reports that things are starting to level out in the industry - but we are still seeing complaints in the region of 2,000 every day coming through."
Unresolved complaints tend to reach the ombudsman a couple of months after consumers have made their initial complaint to their bank.
Barclays said that overall, complaints in the first six months of 2013 were down by 11% on the previous half-year, with a total of 381,740 complaints recorded.
Within this figure, the bank also saw a sharp fall in banking complaints, which have dropped by one third compared with the second half of 2012. Half of banking complaints were being upheld by Barclays in the first half of 2012, a proportion which has now dropped to two in five.
Barclays put its improved banking record in part down to efforts to cut down on the number of customers being hit by unexpected charges. It has received 60% fewer complaints about charges this year so far compared with the same period a year ago.
The bank recently increased a buffer on its current accounts from £1 to £15 before extra charges kick in. The buffer is available to help customers who have insufficient funds in their account, either because they have gone over their overdraft limit or do not have an overdraft.
Barclays said it also texted 130,000 customers in June to alert them that their accounts had gone into these buffers, to help them avoid being hit by extra costs.
Banks are required to submit their complaints figures every six months to City watchdog the Financial Conduct Authority (FCA), which will publish the industry figures this autumn.
Barclays said it now plans to publish its complaints figures every three months, to help it "engage more regularly with customers".