The Governor of the Central Bank has said that most of the customers wrongly taken off tracker mortgages will have received their compensation payments by the end of June.
Philip Lane was speaking in Washington following a meeting of world central bank governors.
Mr Lane said that the Central Bank will publish a report next week which will show that in the first few months of 2018, a lot more people received redress and compensation and some of the banks have almost completed the process.
"By and large, what we've shown now is that this examination is delivering to a lot of those affected," he said.
"We're resolute in making sure that all of those we think have been harmed by this will receive redress and compensation."
He said however that other lenders still have a way to go and that the Central Bank will continue to "press them hard".
Mr Lane said some of the delays were down to technology and accessing old records but that in general progress is being made.
The Governor also warned against overheating the economy.
He said it is important to navigate the good times because they will not last forever and that we must ensure that both the fiscal position and the credit system are in good shape.
Mr Lane warned that overdoing things now could lead to trouble in the future.
"We know from before that managing the good times is so important before the next downturn.In the good years, we have to avoid overheating.
"We have make sure the fiscal position is good shape and that the credit system is in good shape so that we don't overdo it in the good years which leads to trouble the next time there's a downturn.
"The theme of the event here in in Washington was that in the good times prepare for the downturn."
Meanwhile, Fianna Fáil's finance spokesperson Michael McGrath has said the banks must be held to their promise that all customers affected will get their money back plus compensation by the end of June.
"The Central Bank should not tolerate any further delays in this process and needs to insist that all customers receive the appropriate redress and compensation by the end of June as promised," said McGrath.
"The Regulator must ensure that all outstanding issues are addressed including the 'prevailing rate' customers in AIB and Permanent TSB. Banks that miss this deadline should be subject to tough regulatory action.
"Separately, the Governor's warning about possible overheating in the Irish economy is timely and needs to be taken on board by Government. Fianna Fáil has been consistently arguing that we have to make preparations in the good times for the next economic downturn."