Two community libraries earmarked for closure could be saved.
Sutton Coldfield and Aston libraries were due to shut under Birmingham City Council's plans to save £1.9m by 2018/19.
Public consultation and potentially up to £150,000 in a one-off funding pledge from Sutton Coldfield town council has helped the authority change its plans, a spokesman said.
Kents Moat library is still earmarked for closure.
The new proposal will see staffing reduce from "112 to 99 full-time equivalents," which is up from the 88 initially proposed.
However, Birchfield library will open for 21 hours rather than 35 while the Glebe Farm opening hours will go up from 15 to 21 per week.
The Labour-run city council said Sutton Coldfield Library would remain open whilst the authority, the town council, the Library Lobby campaign group and other organisations "work together to see if a long-term sustainable partnership solution can be established".
Aston library would be one of those run by community organisations.
The Conservative leader of Royal Sutton Coldfield Town Council, David Pears, a Birmingham city councillor, said: "We want to keep the library. We want a long-term solution.
"We want assurances in place that money will be well spent. We don't want to spend £150,000 only for it to be closed."
Tier 1 - 35 hours per week
Small Heath, Ward End, Kings Heath, Acocks Green, Sparkhill, South Yardley, Northfield, Balsall Heath, Erdington, Hall Green, Harborne, Mere Green, Handsworth, Kings Norton, Shard End, Quinton, Weoley Castle, Yardley Wood, Sutton Coldfield
Tier 2 - 21 hours per week
Birchfield, Walmley, Kingstanding, Perry Common, Frankley, Spring Hill, Boldmere, Druids Heath, Tower Hill, Sheldon
Tier 2/3 - 21 hours, but would need communities' or other organisations' involvement "to be sustainable"
Stirchley, Glebe Farm
Tier 3 - run by community organisations and the library service would offer support
Aston, West Heath, Bartley Green, Bloomsbury, Selly Oak
The Library of Birmingham was not a community library and not part of the review and Castle Vale library was entirely community-run, the council added.
It said Bloomsbury and West Heath were temporarily closed, but were proposed for Tier 3 provision once operational again.
Council deputy leader Ian Ward said Kents Moat was "being demolished anyway" as part of the Poolway redevelopment.
The new proposals will go before the cabinet on 14 February.