Scottish Labour leader Iain Gray has indicated he would cap council tax rises at one or two per cent if he wins next May's election.
But he warned that any council wanting a rise in order to protect services would have to make a convincing case.
Speaking to the BBC at the Scottish Labour conference, Mr Gray also warned the highest paid civil servants could see their pay cut by 5%.
And he suggested a public sector pay freeze of up to three years.
The SNP has frozen council tax since coming to power in 2007 and has offered to continue the policy beyond the next election.
Mr Gray said while his party did not oppose a freeze, it would have to be "fully funded".
Being interviewed in a live BBC webcast, the East Lothian MSP said the benefit of the freeze to him personally was 75p per week.
He said: "If a council comes to the government, if it was my government, and said 'we need some flexibility to avoid the worst of the cuts', I would listen to them.
"If they could convince me exactly what the beneficial effect of that should be, we should listen to that."
On the level of cap, he said: "I think in the current circumstances, you're talking about one or two percent."
Mr Gray went on to say Scotland's public sector pay needed to be tackled - but stressed the issue must be taken forward with proper negotiation, such as what workers would get in return.
He argued that council body Cosla made a "mistake" in trying to "impose" pay restraint.
"We have to have significant pay restraint, probably close to, or at, a pay freeze," he said, adding: "Certainly over a couple of years, maybe two or three years."
Mr Gray raised concern over top pay in the public sector, pointing to figures claiming that about 900 workers were earning more than the first minister.
He backed cuts, adding: "Something like 5% isn't unreasonable."
Mr Gray said the lowest-paid public sector workers would benefit from his plan for a "living wage" of at least £7.