Among those, the administration said Thursday, are 15 full-time and two part-time jobs at a school-readiness program for children, and with programs that help refugee youths and families. The workers should be able to find other positions in the county, but about 860 children and 393 refugees will no longer receive services from the programs, which are funded by a state grant that has been cut.

Gimenez’s $5.9 billion budget, down from nearly $6.2 billion last year, was boosted by a small increase in countywide property values, and relies on savings from an administrative reorganization the mayor began implementing this year.

Though Gimenez would like to continue requiring that county employees pay an additional 4 percent of their base pay toward healthcare costs — bringing their total contribution to 9 percent — several commissioners nixed that idea, including the swing vote, Barbara Jordan. Gimenez has set aside $23 million in his proposed budget to fund the difference.

“If the vote remains the same, then the four percent will go back” to the employees, Chairman Joe Martinez said.

But the board did not officially make a decision on the matter Thursday. Gimenez said his administration is negotiating with several unions to redesign employees’ health-insurance plans to avoid looming hikes in dependent premiums. The mayor said he would like to present that proposal to commissioners as early as next week so they have more information before taking action on the 4-percent healthcare contribution.

“I would hope to bring it up almost as a package deal,” Gimenez said.

In July, the board agreed with Gimenez’s proposal to lower the property-tax rate by 2 percent, to $9.55 per $1,000 of taxable assessed property value. In an unincorporated neighborhood like Kendall, the owner of a $250,000 home with a $50,000 homestead exemption would pay about $38 less in county taxes than last year.

But if a property’s value rose more than the nearly 2 percent countywide average, a homeowner could see a slight uptick in county taxes, which represent only a portion of their total tax bill.

Under state law, the county will still have to post a notice of “tax increase” because it will receive more in total tax revenues than last year, given the rise in property values.

Gimenez has characterized his budget as a continuation of the one commissioners approved last year. It spares most services, and restores funding for programs at the Miami Science Museum, Miami Art Museum, HistoryMiami and the Vizcaya Museum and Gardens to levels they haven’t seen in six years.

The budget also proposes recruiting new firefighters and hiring the first two classes of police officers in three years. Gimenez’s financial plan also calls for the elimination of 60 vacant, non-sworn positions in the police department, which the mayor said will not affect street patrols.