Two more Labour-led councils have voted to voluntarily freeze the basic rate of council tax.
North Lanarkshire said it would not pass what it called government cuts on to residents.
Stirling, which also has a Labour leader, said it had voted to freeze council tax "to protect the pockets of Stirling residents".
It takes the number of Labour-led councils to back a freeze to eight. Most councils have opted for 3% rises.
The eight Labour-led councils to confirm voluntary council tax freezes are:
- South Lanarkshire
- North Lanarkshire
- West Lothian
- West Dunbartonshire
All those councils have Labour leaders.
Residents whose homes are in property bands E, F, G or H will still see their bills rise as a result of national changes.
However, the freeze in basic bills will inevitably add to the pressure on these council's finances.
The leader of North Lanarkshire Council, councillor Jim Logue, said: "There has been much speculation about the council's ability to raise council tax by up to 3%.
"However, the Scottish government have already increased substantially the amount people in Bands E to H will pay.
"That means households in Band E will have their bill hiked by 7.5%, rising to 22.5% for Band H households. We are not prepared to put more pressure on struggling families, so there will be no council-imposed increase.
"This is a budget which invests where it is needed most: more money for vulnerable older adults, more money for vulnerable young adults with complex needs and more money to head teachers to determine expenditure directly according to the specific needs of the communities they serve."
Stirling Council leader Johanna Boyd said: "This budget aims to protect the vital services Stirling Council provides while ensuring that we also protect the pockets of Stirling's residents.
"We are dedicated to improving Stirling's urban and rural infrastructure and our commitment to fund various capital projects over the coming year will mean that various areas will benefit.
"Our City Region Deal will also provide a huge boost to both the local and national economy, and over the next 12 months funding will be provided for projects to support this."
Three other councils, East Dunbartonshire, East Ayrshire and Argyll and Bute, on Thursday agreed to 3% increases in the basic rate of council tax. Three more, Dumfries and Galloway, North Ayrshire and South Ayrshire, have still to set their rate.
Critics may say a council tax rise would at least help to reduce the pressure on finances and help mitigate any cuts in services or savings targets.
Supporters of the Scottish government would argue a council which freezes council tax may find it hard to argue convincingly that it gets too little government cash.