CASH-strapped City of York Council has found savings that could cut its budget shortfall by £3.5 million.
Financial experts have already identified £2.8 million which can be shaved from the initial £4.7 million shortfall the authority faces next year.
And council leader Rod Hills reckons that can be further reduced to £1.2 million.
But Coun Hills warned the savings would mean cuts in services, and huge council tax rises were still likely.
He said: "We have asked the departments to look very closely at what they're doing and how they're doing it, and where they can make savings.
"These savings will inevitably have some impact on services, and we would still be £1.2 million short. That is likely to mean very significant increases in council tax."
The potential cuts have not yet been approved by the council, or made public.
But, if approved, Coun Hills estimates an increase in tax revenue of £400,000 would be needed.
He said: "I can't see any way around it but to have a big increase in council tax."
Government figures allow City of York Council to spend up to £136 million next year - an increase of £7.9 million. But the Government grant has risen to only £90.7 million.
Consultation with city residents has suggested most would rather pay extra tax than face cuts in services.
A questionnaire circulated at ward committees in October showed 67 per cent of respondents wanted to increase council tax by five per cent if that would keep services at the level they are now. This is the level of increase recommended by the Government.
But Coun Hills said the increase is likely to be more than that.
North Yorkshire County Council has already announced that its council tax payers are expected to face a rise of 10.25 per cent - equivalent to an extra £1.31 a week on the average band D property.
Final budget decisions will be made in February.
Updated: 10:12 Monday, December 31, 2001
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