An updated plan for cuts to the Miami-Dade County budget would keep open six of 22 public libraries initially slated for closure.

The tentative change would save the Culmer, Lakes of the Meadows, Lemon City, Little River, Opa-locka and Shenandoah branch libraries, bringing the total number of library closures to 16.

Amid uproar over Mayor Carlos Gimenez’s proposal to shut down nearly half of the county’s 49 libraries, administrators have been drafting alternatives to make the budget cuts a little less painful. A final plan won’t be approved by county commissioners until two public hearings on the budget in September.

Lisa Martinez, a Gimenez senior advisor who oversees the library department, said Tuesday the administration will continue looking for savings.

“This is the first swipe at the list,” she said.

Her team is examining how libraries may be able to save on staffing and other costs, such as information technology expenses, to make room in the budget. About eight million people visited a Miami-Dade library last year, according to the county, and another five million visited its website.

Commissioners voted two weeks ago to keep the property-tax rate flat for the 2013-14 fiscal year, following Gimenez’s last-minute recommendation, which called for the closure of 22 libraries, the elimination of six fire and rescue trucks and the layoffs of 400 county employees.

The mayor had originally called for raising the tax rate to maintain library and fire-rescue services and avoid layoffs. But he reversed course after hearing outcry over a potential tax hike, two years after his predecessor, Carlos Alvarez, was recalled in the wake of an unpopular tax-rate increase.

Since the July 16 vote, commissioners who favored the flat tax rate have worried about shuttering so many libraries. Some have called for renegotiating leases for libraries located in private, commercial storefronts, or moving those branches to existing public facilities that would not charge rent.

On July 22, Commissioner Xavier Suarez proposed that the libraries on the hit list housed in buildings owned by the city of Miami — at the time, Culmer, Lemon City, Shenandoah and Virrick Park — work with city government to stave off the closures.

For the Virrick Park branch in his district, where the city already waives the rent, Suarez said his office would pay for two full-time staffers and a part-time supervisor for a year. If the city agrees to waive the $22,000 in janitorial fees, Suarez wrote, perhaps the library could remain open.

Landlords in other commercial storefronts might also be coaxed into waiving or reducing the library rents, Suarez suggested.

Two days later, Commissioner Esteban “Steve” Bovo, calling libraries “a lifeline to many in our community” asked for details on the Palm Springs North branch targeted for closure in his district and suggested nonprofit organizations might be willing to house libraries and charge lower rents. Libraries could consider engaging in some sort of commercial activity, such as selling books or food, to make money, he added.

“We need to assure residents that the level of service they have come to expect and rely upon will not be compromised,” Chairwoman Rebeca Sosa said in a memo to the mayor Thursday.

Responding to commissioners that same day, Gimenez said he welcomed their recommendations, “but all scenarios must be vetted against criteria that evaluate the fiscal and programmatic viability of a sustainable county government,” he wrote, highlighting “sustainable” in bold.