Council tax will rise by about £50 for the average household in both Bath and Somerset after budgets were approved by councillors.
Bath and North East Somerset Council (Banes) cut £9m from its budget, described by one cabinet member as a "masterpiece".
But opposing Liberal Democrats said the savings would "slice into the bone".
Somerset County Council also agreed its £328m budget, which had support from the opposition Lib Dems.
Banes finance chief Charles Gerrish said: "We are proposing a level of council tax needed not only to balance our budget but also to sensibly invest in our long-term financial sustainability.
"We will protect the majority of frontline services and provide additional investment into services for vulnerable residents."
Transport and environment cabinet member Mark Shelford described the £113m budget - including a 2.95% council tax rise, meaning a £50 increase for the average household - as a "masterpiece" in the circumstances.
But Liberal Democrat group leader Dine Romero said: "Residents are going to be paying far more for far less.
"This is no longer a budget that simply cuts the fat. This now slices into the bone, the structures that support and protect the most vulnerable."
Councillors from other parties also condemned the budget, with some calling for it to be refused.
In Somerset, the council budget was set to £328m for the next financial year, including a 2.99% council tax hike.
Politicians also backed a Lib Dem motion to make the whole county carbon neutral by 2030.
Conservative council leader David Fothergill said: "There have been some very tough decisions along the way, but we are in a much stronger position than we were earlier in the year."
Liberal Democrat Liz Leyshon said: "Having turned the corner, the challenge now is for us to stay on the straight, hopefully not too narrow, path."