community groups hoping to save Bilton Library will be given until April to devise a plan.
Coun Chris Metcalfe, executive member for libraries, said the council must be given a firm commitment by October 31 if the facility is to stay open.
Volunteers will then have until April to put together a detailed business proposal.
Bilton is one of eight “category three” libraries which will lose council funding from April.
Coun Metcalfe told the Advertiser: “Bilton and all those other communities have so far demonstrated a real interest in forming an action group to save the library.
“What we are saying to them is: ‘We will work very closely with you, advise you and put you in touch with people who will assist you.
“What we are looking for by October 31 is a very clear demonstration of that commitment to find a community solution.
“I need to know that all eight communities are up for it.”
He said there were two groups in Bilton “demonstrating very clearly that they want to be involved” via separate proposals, and the hope was that they would work together.
A short extension to the April 2012 cut-off point would be possible if the construction of a business plan was well under way by that time, he added.
Last week, members rejected Coun Bill Hoult’s proposal to give all eight under-threat libraries in the county a six-month extension to produce their business plans, which would have cost the council an extra £180,000.
Coun Hoult said he welcomed the thrust of the revised council measures published in June - retaining some support for Starbeck Library, among others - but thought threatened libraries needed more time.
“This proposal is just to give people a bit more time to come together to find a solution,” he told members.
Coun Andrew Goss added: “It is most important that we give them that chance to create a library which volunteers can run and which can be of benefit to the community.”
But after a report from the executive member, who said there was no need “to commit any further resources to this project”, Coun John Blackie said he trusted Coun Metcalfe and the libraries service and there was no need to formalise the arrangements any further, a view reflected by the council vote.