Leaders at Carmarthenshire Council said they have tried to listen to the public after dropping plans to close public toilets, reduce specialist youth support and raise cemetery charges in this year's spending plans.
Many people objected to the proposals in a budget consultation, which could have seen the closure of public toilets in St Clears, Ammanford and Llanelli Town Hall in 2021-22.
The cemetery proposal only related to the Ammanford burial site on Dyffryn Road.
The Plaid Cymru-Independent administration has also scrapped planned increases in leisure service charges and will meet the shortfall by encouraging more uptake.
In a further announcement at an executive board meeting on February 24, it will invest an extra £428,000 - on top of its existing spending plans for 2020-21 - into social care, education and road improvements.
And it won't close Whitland household waste recycling centre in 2021-22.
It has also deferred two other money-saving measures, relating to additional learning needs and residential placements, to 2022-23.
Cllr David Jenkins thanked the 2,000-plus people who took part in the consultation.
"I, as portfolio member for resources, and member colleagues have again really tried to listen both to the public and fellow members’ concerns and respond accordingly," he said.
The council's net budget for day-to-day services in 2020-21 is £371.6 million, which reflects a better than expected settlement from the Welsh Government.
But this provisional settlement, which includes a share of business rates, requires a £97.4 million take from council tax.
This will mean a 4.89% rise in council tax from April 1, taking the average Band D property in Carmarthenshire to £1,316.55.
Schools will get an extra £10.1 million which, taking into account inflationary costs, will give them the same spending power as currently.
The budget will be set by full council on March 3.
The day-to-day budget for the current financial year is £351.3 million, but an overspend of £2.75 million has been forecast. This could end up being plugged by money held in reserves.
The council's spending plans budget for a 2.75% staff pay rise in 2020-21 which, combined with increased pension costs and other factors, creates significant inflationary pressures and therefore the need to make ongoing savings.
Cllr Glynog Davies, executive board member for education and children, said he was "far happier" than he was this time last year.
He added: "The best resource is good staff, who are dependable and conscientious."
Average council house rent rises of 2.7% - or £2.36 per week - are proposed in 2020-21, along with a £34.7 million programme of maintenance and upgrades in council housing stock.
But Cllr Peter Hughes-Griffiths said the funding on its way from central Government in 2020-21 was a real-terms reduction, despite being 4.4% higher than the current year.
Referring to the proposed balanced budget, he said: "What we have succeeded to do is miraculous, in a way."
