But councillors didn't support closing libraries on Mondays and Tuesdays, or ending late nights.
Instead, they asked staff to look at reducing operating hours of community libraries by a total of 25 hours.
That will mean no changes to the two busiest libraries in Garden Place and Chartwell. The libraries will also continue their usual weekend hours.
Councillor Gordon Chesterman told the meeting tampering with the operating hours would be like giving the service a triple bypass.
Councillor Ewan Wilson said the changes were a compromise and far more palatable than the initial proposals.
The council's $1.5 million book collections budget will be reduced by $200,000, instead of the suggested $500,000.
Hamilton library director Su Scott said a $200,000 reduction would not have a visible effect on the book collection whereas reducing it by half a million would result in a "shrinking and ageing" supply of books.
Other changes include increased charges for reserved books and late books, which the council passed without challenge.
It did not cancel $80,000 for the Maori and Pacific Project because that would send the "wrong signal" to the community .
Meanwhile, charges for burials at council-run cemeteries will rise by $168.25 and cremations will rise by $55.
Residents and ratepayers will get their say on the draft plan in March.
SERVICE SHAKE-UP
Increases
* Late library book: 50c a day
* Late reserved book: $2.50 a day
* Cremations: up $55
* Burials: up $168.25
Cuts
* Twenty-five hours a week to be shaved off community libraries.
* Book renewals budget reduced by $200,000
What stays
* $80,000 Maori and Pacific Project Fund
* Weekend and late-night library opening hours