Swansea householders affected by recent flooding won't pay council tax for up to a year.
Council leader Rob Stewart said a six-month exemption would apply for people whose homes were flooded, with a 12-month exemption for people who have had to move out because of the damage caused.
This would be on top of a Welsh Government pledge of £500 for every affected household - or £1,000 for those without home insurance cover.
His announcement at a meeting of full council came before councillors set the budget for 2020-21, which included a 4.58% council tax rise.
Swansea escaped the worst of Storm Dennis but more than 40 properties were flooded in Gorseinon, and a further eight in Penllergaer.
Cllr Stewart praised Gorseinon councillor Kelly Roberts for her hands-on efforts in the aftermath of the awful weather.
"You have set an example to us all," said the Swansea Labour leader.
The council's core budget for day-to-day services next year will be £468.6 million, £25 million more than currently.
This will be financed by an extra £17 million from the Welsh Government and an extra £8 million from council tax.
However, the council is said to be facing £35 million of additional cost pressures - such as staff pay and demographic demands - meaning that nearly £10 million of savings and income-generating measures will be enacted.
There was cross-party support for the extra money coming from central Government which, combined with the administration's spending priorities, will boost schools spending by £9.7 million and social services by £8 million.
But there was disagreement over the 4.58% council tax hike.
The Liberal Democrat-Independent opposition put forward a costed amendment to reduce the council tax rise to 3.56%, worth £1.26 million.
Lib-Dem leader, Cllr Chris Holley, said: "When we have got a bit more money, surely we should help the council taxpayers as well?
"That would be a gesture towards the public."
Independent councillor Wendy Fitzgerald added: "It is completely unacceptable that council tax goes up year after year - until the election, when it goes down."
Labour members hit back, with Cllr Stewart saying the previous Liberal Democrat-led administration had frozen council tax in an election year. He said this had created a £40 million loss of revenue over the subsequent seven years.
Other Labour councillors criticised the spending measures which the opposition proposed to cancel in order to fund some of the amendment.
And there appeared to be some confusion about where most of the money would come from.
The amendment said £1 million of the £1.26 million would come from general reserves, via a contingency fund. The Lib-Dems said their intention was to divert this £1 million from going into a capital equalisation reserve, which the administration has been building up to pay back borrowing costs for the Swansea indoor arena project.
Cllr Peter Black, of the Lib-Dems, said: "You are putting up council tax now to fund that borrowing in advance."
Cllr Stewart strongly rejected this.
"There is not a penny of council tax being used to repay borrowing," he said.
The Labour leader said half the council tax rise would fund day-to-day cost increases, with the other half going to schools and community projects.
Labour councillor Mary Sherwood said her party was looking after the most vulnerable members of society, and added that people on the lowest income wouldn't be affected by the council tax rise.
Cllr Peter Jones, meanwhile, branded the amendment "silly". He said the £13.71p per year council reduction it would generate for band D householders was "a trivial amount".
Cllr Paxton Hood-Williams, of Swansea Conservatives, said the Welsh Government had not passed on the level of funding to councils that it had received in recent years from Westminster.
"It is the Welsh Government alone that has caused austerity," he said.
Labour councillors strongly disagreed, saying austerity had come via Westminster since 2010.
Cllr Louise Gibbard quoted a series of findings from recent reports, including one which said life expectancy for some people had stalled and even reversed.
"I can't contain my anger at the past, lost decade and its likely impacts in the years to come," she said.
The revenue budget was approved by a majority, with opposition councillors abstaining.
Among the other spending pledges the budget contains are an £8.4 million investment in roads, pavements and street lighting, a £1 million fund for community projects, free wi-fi to be rolled out in outlying commercial areas, a £1.75 million Wind Street investment, and more money on cleansing teams.
Also passed, this time with minimum debate, were the capital and housing revenue revenue budgets for 2020-21.
Cllr Stewart urged the UK Government to continue providing extra funding to local Government, as it has for 2020-21.
He spoke warmly of a recent meeting with the new Secretary of State for Wales Simon Hart and his deputy.
"It was a breath of fresh air, compared to his predecessor," said Cllr Stewart.
"I look forward to a productive relationship."
