Dorset County Council will increase its share of the council tax by just under 2% next year.
It already need to cut £15 million this year and the council says it would have to save even more if they didn't increase their share of the council tax.
Council tax payers in Devon will find out how later today how much they'll be paying for services next year.
The local authority needs to save £46 million.
It's hoped there may still be extra investment in schools when it meets to set its budget today.
Council tax in Swindon is set to remain frozen for the fifth year in a row.
The recommendation to keep it at its current level will go before cabinet members next week, when they are due to decide on next year's budget.
Somerset County Council today announced that people whose homes are flooded or cut off because of the floods will not have to pay the County Council part of their council tax until they are back in their homes.
Leader of the Council, Cllr John Osman, said: “We recognise that local people affected by the flooding are struggling and under tremendous strain.
“We want to remove one of their financial worries by suspending their council tax charge while they are stranded or unable to live in their home.
“There are some people who are being asked to pay council tax both on their home that they have had to leave under traumatic circumstances, and also where they are now in emergency accommodation. That can’t be right and we are reacting quickly to reassure people.
“We are in talks with our District Council colleagues to see if they are able to follow our lead and also suspend their part of council tax for flood victims.”
Council tax in Plymouth will rise by 2% from April after a government grant was cut by nearly 8%.
The Labour controlled Council rejected a move to freeze bills as it has done for the past two years. It will increase all its employees wages to a 'living wage' of at least £7.20 and hour an spend £166 million on capital projects in the next four years.
Councillors in Cornwall have voted to freeze tax bills in the county.
Council tax in North Somerset will rise by 1.5% in the year ahead.
The decision was made at last night's [Tuesday] full council meeting. The rise equates to a 33p a week rise for an average Band D property, with an annual bill of £1,164.88 - a rise of £16.95.
Challenging finances are not new to us. We are a low-funded and low-spending authority and have successfully dealt with previous budget reductions.
However, we have never faced such challenging times as now, and they will be with us for years. The scale of change will be significant and the council will look, feel and operate very differently in the future. Despite this, our vision and ambitions remain the same
Councillor Ashton added that government grant funding had been reduced by 6.3% for 2013/14 but that the council is still waiting for confirmation of the final settlement. He added that it is because of unfair funding that the decision to raise council tax has had to be taken.
We have considered the proposals put forward in the alternative budgets by opposition groups, each of which suggested a 2% tax rise, and we have also examined the freeze grant the government is offering. However the numbers just don't add up, which is why, with some regret we are making this increase.
Full details of the council tax amounts by council tax band and parish can be found here.
Cornwall faces drastic cuts in frontline services, which could lead to the loss of libraries and leisure centres. That's the stark warning from senior council officials, who say the only way to avoid the cuts is to increase council tax and reduce the funding for those claiming benefits.
One councillor said it was scaremongering and there were other areas where money could be saved. Our Cornwall correspondent Steve Hardy reports.