Lloyds Banking Group has been cutting the compensation it pays to payment protection insurance (PPI) claimants, a BBC investigation has revealed.
PPI expert Cliff D'Arcy told the BBC Lloyds had saved more than £60m over the past year by cutting compensation.
Lloyds refused to be interviewed on the issue. It was offering the correct level of compensation in line with regulatory guidance, a statement said.
Lloyds cites a little-known regulatory provision called "alternative redress".
Alternative redress - also known as comparative redress - allows a bank, in specified circumstances, to assume that customers to whom it wrongly sold single-premium PPI policies would have bought a cheaper, regular premium PPI policy instead.
In such cases, a bank is entitled to deduct the cost of the regular premium policy from the full compensation they would otherwise have had to pay.
For claimants, this deduction can make a large difference to the compensation Lloyds offers.
Mr D'Arcy, who previously worked at HBOS's PPI operation, told BBC Radio 4: "Frankly I'm amazed that this problem has existed throughout the last year and hasn't emerged into the light."
Care worker Veronica Rayner had two loans from Halifax, now part of Lloyds Banking Group.
Mrs Rayner told the BBC that when she had taken out her loans she had been unaware that the bank had sold her PPI policies as well.
Her £2,300 compensation offer from Lloyds was set out in a seven-page letter with an additional two-page appendix of calculations.
Mrs Rayner said she hadn't realised from the offer letter that the bank had applied alternative redress to her claim.
But after her claim was referred to the Financial Ombudsman, Lloyds was told to pay her an additional £1,200 of compensation - over 50% more than it had originally offered.
"I don't think it's very fair. I think they should just offer people the right amounts and get it done. It's cheating people in a way," Mrs Rayner said.
Lloyds told the BBC 11% of offers it made in the fourth quarter of 2013 on loan complaints were made by applying alternative redress.
Analysis of a large survey of PPI offers undertaken by the PFCA, a trade body representing claims management companies, suggests in some months more than 25% of Lloyds's offers were made by applying alternative redress.
But Lloyds told the BBC only 5% of offers made last year were made in this way.
Mr D'Arcy told the BBC such use of alternative redress was unjustifiable. He said such reductions could legitimately be applied in fewer than 1% of PPI cases.
"A taxpayer sponsored bank is depriving taxpayers of their rightful compensation by using a loophole. It's a scandal coming out of a scandal," he said.
Claims management companies have told the BBC they have routinely been challenging alternative redress offers from Lloyds by referring them to the Financial Ombudsman Service.
Martin Baker, of Swindon-based company Renaissance Easy Claim, said the ombudsman had so far ruled on more than 100 of his clients' cases.
"In every single case our challenge has been upheld, and clients will now be entitled to full redress," Mr Baker told the BBC.
Mr D'Arcy is unsurprised that so many offers are being overturned by the ombudsman.
But he warned that, since nine out of 10 PPI compensation offers were not referred to the ombudsman, most of Lloyds' alternative redress offers were likely to go uncontested.
As a result, Mr D'Arcy told the BBC, "Lloyds is making substantial savings of millions of pounds a month, and customers are being short-changed".
Lloyds Banking Group has refused to say how many alternative redress offers were made in total last year or by how much offers were reduced as a result.
But in a statement it said: "The numbers that have been provided to the BBC by the claims management companies are incorrect and deeply misleading.
Since we started making comparative redress offers last year, that equates to 5% of the total number of complaints that we have dealt with.
For these, we have used a formula agreed with the Financial Conduct Authority. The overturn rate for loans claims is the same whether it is for comparative redress or for other reasons."