A below inflation council tax rise of one per cent is being proposed for 2019/20 by Central Bedfordshire Council, without cuts to front line services.
But the local authority plans to consult its residents to see if there is any enthusiasm for a further one per cent increase.
It first increased council tax three years ago after a change to the way local authorities are funded.
The council achieved £105m of savings during the seven years prior to 2016/17.
Since Central Bedfordshire Council was formed in 2009, around £135m of efficiencies have been delivered, according to a report to its executive.
Arlesey councillor Richard Wenham said: “This budget has been prepared against a background of continuing austerity, with our revenue support grant this year now reduced to zero.
“Pressures continue in children services, the care of old people and disabled adults.
“But the actions we have taken have contained the rapidly growing homelessness issue, which followed the introduction of the Homelessness Act last April.
“New and unforeseen challenges have appeared, including a £1m pressure from the disappearance of recycling income, after China’s decision to stop accepting used plastic material.”
The draft budget has been prepared before the final announcement of the local government settlement, according to Cllr Wenham, executive member for corporate resources and deputy leader.
“There may be some minor revisions when we come back in February,” he warned.
“At a time of slow wage growth, this regressive tax will continue to impact on many of our residents.
“In Central Bedfordshire, we recognise that impact and, as always, are looking to keep our increase to the minimum necessary, while ensuring delivery of high quality services.
“And as a result the central case of our budget is a planned one per cent increase in council tax, less than half the current rate of inflation.
“In our consultation we have also included questions about the proposed increase in general council tax, but also the appetite for an additional one per cent to gain feedback from our residents on the balance of council tax against local services.
“We will be looking in detail at the consultation responses and feedback from scrutiny and from members, before finalising our recommendation to councillors at February’s meeting.”
Cllr Susan Goodchild asked: “If our residents decide that they would prefer to pay a higher rate of increase than one per cent, can I seek assurance the residents’ views will be considered?”
Leader of the council James Jamieson, who chairs the executive, described it as “another excellent budget proposal”.
He said: “We see ourselves yet again in a position where we are maintaining, if not enhancing services to our residents and proposing a sub-inflation council tax increase.
“Other local authorities are shutting tidy tips, or massively increasing car parking fines, or looking at various other fairly extreme measures to make their budget add up. We are in a good position that we have managed to avoid these things through very good management by our officers and by members.”
The budget will go out to consultation and be considered by the council’s corporate resources overview and scrutiny committee.