Council tax payers in Wales should not see "excessive" rises in their bills next year, says assembly Finance Minister Sue Essex.
Sue Essex says no-one will move up more than one band in a year
She said the money councils would receive was "fair and reasonable".
But one in three homes will move up a tax band with revaluation, higher than the original estimate of one in four.
But the Welsh Local Government Association said the settlement would mean councils had to cut services or raise tax.
Ms Essex said £11m would be allocated to councils to ensure no-one moved up more than one band in a year.
She also announced a scheme where councils can
keep £13m worth of business rates.
The big winners in the settlement were Monmouthshire, which will get 7.1% more, and Bridgend and Blaenau Gwent, which see a 6.3% rise.
Cardiff, Gwynedd, Conwy, Merthyr, and Wrexham see the lowest increases, at 3.5%.
"The great volatility, with council tax going up and going down doesn't make a lot of sense to the public, and that's why we've tried to work with councils on this," she said
Councils say they will have to make cutbacks
"I don't feel, overall, this should give rise to excessive council tax increases."
But Alex Aldridge, leader of the Welsh Local Government Association, said councils faced "some very hard choices" between service cuts and raising
He added: "The assembly has chosen to make the health service a priority this year, but this means that there simply won't be enough left for local government."
Opposition parties criticised the settlement, saying council tax increases were likely.
Plaid Cymru's Dai Lloyd said: "This latest local government settlement is disappointing. It will be particularly difficult for local government to meet
its service commitments in this settlement.
"Local government, unlike the National Assembly for Wales, has the power to raise its own tax - council tax.
"Faced with a disappointing settlement, pressure
will be on councillors to raise the council tax to preserve and develop services, such as social, education and housing.
'Massive double whammy'
"The choice will be a difficult one of raising council tax, or cutting services, or raiding council reserves.
"For local taxpayers already faced with a significant tax hike by council tax re-banding and revaluation, they will face a double whammy of an increase in council tax or a cut in services."
The Conservatives' leader in the assembly, Nick Bourne, said: "For a lot of Welsh councils,
the figure is well below 5%, and it comes on top of a re-banding exercise which has meant a massive double whammy for many families.
"This is exactly what we predicted would happen, with taxation through the
back door, paying for these pet projects."
But Welsh Secretary Peter Hain said: "I am
particularly pleased that Welsh local authorities will benefit from a scheme
which allows them to retain a part of the business rates that are collected when
the local economy is growing."
The scheme would be worth £60m over the next three years, he said.
Mr Hain added: "I hope that this will help Welsh councils to keep council tax rises very low over the next few years.
"This is very good news for Wales and shows what working together can achieve."