Vale of Glamorgan Council says it will consider a 1% cut in its proposed council tax rise for the next financial year.
The local authority had been planning a 6.9% hike, as it sought to make nearly £9 million in savings.
It means Vale Council is set to receive an extra £1.1 million.
The cabinet will meet on Thursday to discuss whether the final budget should include a revised 5.9% increase in council tax, before a final decision is made at a full council meeting on 10th March.
Council leader Lis Burnett said: "We have consistently made (the) Welsh Government aware of our misgivings with its funding formula, which sees the Vale of Glamorgan receive one of the lowest financial settlements in Wales."
“I’m pleased that those representations have been considered and that our funding will increase from 3.3 per cent to 3.8 per cent compared to last year."
“I said the last time our draft budget proposals were considered by the council’s Cabinet, it was with a heavy heart that the recommendation was for a council tax increase of 6.9 per cent."
"That was not something I was comfortable with and not where we wanted to be as an administration This additional funding offers the chance to significantly reduce that initially proposed increase."
“I believe it is right that we use this money for that purpose, rather than reduce savings targets or make the budget easier to manage, as this reflects the priorities of our residents who expressed concern over council tax increases in our budget consultation. It is only right that we respond to that concern.”
The Welsh Government's annual settlement makes up for two thirds of the council's overall funding, with the rest made up of council tax contributions and a share of business rates from across Wales.
The council insists the proposed 5.9% hike will be smaller than that introduced by most other local authorities in Wales - with residents still paying considerably less than the national average.
But despite a relatively last-minute cash boost from the Senedd, the council still says it's facing an "extremely challenging" position financially, amid growing demand for critical services, particularly care.
71% of next year's budget is earmarked for schools and social care, which have both seen an increase in their funding to record levels as part of the council's strategy to protect services for the Vale's most vulnerable residents.
Cllr Burnett added: “We have been operating within incredibly challenging financial constraints for several years. Despite this, we have a track record of continuing to deliver our most vital services to a very high standard."
“Prioritising investment in social care in recent years means that the Vale has the fewest delays in hospital discharge in Wales and we are able to source home care for those who need it in an average of three days."
“Continued investment in our schools means our pupils learn in some of the most modern facilities and those that need additional support can access excellent provision."
“We will continue to invest in our children to make sure they are given the very best platform for success and maintain support for those in the greatest need.”
A four-week public consultation has already taken place on the budget proposals, alongside a number of scrutiny committe meetings.
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