Deputy Prime Minister Nick Clegg has signalled that the UK Government will agree to Scottish Government demands which will effectively put an end to the so-called bedroom tax north of the border.
The SNP administration had requested that a cap on payments which can be used by councils to support tenants affected by the housing benefit change be lifted, allowing it to fully mitigate its impact.
Mr Clegg's comments came as Scottish Liberal Democrat leader Willie Rennie said the "bedroom tax" should be scrapped because it is not working as intended.
Both leaders are in Aberdeen for the Scottish party's spring conference.
Mr Clegg said: "I actually strongly agree that of course a policy like this needs to be kept under constant review and should of course be amended and changed as things go along.
"There are some changes that we can deliver in this coalition Government and frankly there are some that the Liberal Democrats can't because of the Conservatives."
The "bedroom tax", or spare room subsidy, involves cutting housing benefit from social housing tenants with spare rooms. Councils can make discretionary housing payments (DHPs) to those tenants who are at risk of falling behind in rent and getting into debt as a result of the change.
The Scottish Government says UK Department for Work and Pensions (DWP) rules mean it is constrained in what it can legally spend on DHPs, and it has written to the UK Government requesting this cap is removed.
Mr Clegg said: "There are some councils in Scotland who have run up to the limit of the funds they have available to them for discretionary housing payments.
"There is this limit - a cap in effect - on what councils can use which I think needs to be addressed, and we will be making an announcement about that shortly.
He continued: "This is obviously a highly controversial policy, it is one we are constantly keeping under review.
"It is one that I have insisted there are more funds available to deal with the hard cases. I am confirming there will be an announcement from the coalition Government in dealing with this issue of the cap that in effect prevents Scottish local councils from using the money as freely as they wish."
Earlier, when asked during a BBC interview if the "tax" should go, Mr Rennie said: "I don't think it should stay."
He said: "The principle behind (the spare room subsidy) I can understand but, to be honest, I don't think it is working as it was intended and I think it should just go, and it should go quickly."
At last year's Scottish Lib Dem conference, Mr Rennie had stood by the controversial policy.
"The bedroom tax is tough, but it is central to the welfare reforms," he told activists in Dundee last March. "If we believe in the principle of making work pay, we need to reform the welfare system to be able to cover that."
Mr Rennie said his party is working with housing associations to make sure people do not suffer unintended consequences, and is "sensitive" to concerns.
"I have met lots of people who are really, really anxious about it, and I don't want anyone to suffer, but we need to get the right people in the right places," he said.
Party members in Dundee had called on the coalition Government to defer the under-occupancy rules and reconsider its approach.
Just one Lib Dem openly backed the Government policy at the end of a debate on the emergency motion last year.
SNP MSP Linda Fabiani, who sits on the Scottish Parliament's Welfare Reform Committee, said: "The Lib Dems have only themselves to blame for getting us into this situation in the first place - rushing headlong with the Tories into Government and inflicting the bedroom tax on the people of Scotland.
"Scottish Government ministers have repeatedly raised the issue of discretionary housing payments with counterparts at Westminster.
"Only a Yes vote and independence will give the Scottish Parliament the power to scrap the bedroom tax - in the meantime, the Lib Dems and Tories should get out of the way and let the Scottish Government get on with the job of mitigating the bedroom tax for all those affected."
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