A contentious healthcare concession imposed earlier this year on Miami-Dade’s nearly 26,000 county employees will almost certainly be history Thursday night after commissioners sign off on a new budget.

But the county won’t be done wrestling with rising healthcare costs.

Mayor Carlos Gimenez’s administration has warned employee unions that, beginning Jan. 1, health-insurance premiums for their dependents, such as spouses and children, will rise 20 percent. The hikes could be avoided, the administration says, if the unions agree to “redesign” the health-insurance plan to raise co-pays for doctor visits and prescription drugs.

The redesigned plan would save the county about $14 million, Gimenez said.

“We have no desire to impose a 20-percent increase in premiums,” he said, calling the redesigned plan still “more than affordable.”

“I think it’s good for the employees,” he said. “I think it’s good for the unions.”

Under the most popular plan the county offers, the co-pay to see a primary-care doctor would increase to $15 from $10. The co-pay to see a specialist would rise to $30 from $10. And a 30-day supply of prescription drugs would go up to $15 from $10.

The alternative for that same plan: hiking bi-weekly premiums for family coverage to $345 from $288.

Under either scenario, the county would continue paying HMO premiums for its employees.

Regardless of what happens with the insurance plans, employees will likely get some good news: When the new budget year begins Oct. 1, they will probably no longer be required to contribute an additional 4 percent of their base pay toward healthcare costs. A narrow majority of commissioners imposed that concession in January, on top of the 5 percent of their pay that employees already contribute toward healthcare.

A majority of commissioners have made clear that they want the 4-percent giveback to go away for the 2013-14 fiscal year. Gimenez wanted to keep the concession, but seeing he did not have the votes on the dais to do so, budgeted $23 million to eliminate it.

The healthcare plan, however, would still need to be redesigned because of higher costs, Gimenez said.

Earlier this year, his administration had tied getting rid of the 4-percent giveback to raising health-insurance co-pays and making coverage for dependents more expensive. Six scenarios unveiled around May — which one union president at the time called “the nightmare list” — proposed lowering the concession and, for example, increasing the cost of seeing an in-network specialist or adding a deductible to a popular HMO plan that does not currently require one. Another scenario increased premiums for spouses and children by 20 percent.

Those scenarios have since been discarded. Gimenez has said the county, which saw a better-than-expected uptick in property values, can afford to eliminate the concession without tying it to the healthcare plan. But, separate from the concession, the county says its healthcare costs over the past two years rose about 20 percent — which would be passed along to employees as higher dependent premiums.

That 20 percent comprises a nearly 12-percent increase in healthcare costs last year and an 8 percent increase this year. The county agreed not to raise premiums last year — but that was a one-year deal, Gimenez said. Now, the county needs to make up for that by passing along last year’s and this year’s higher costs to employees, in the form of 20-percent dependent premium hikes.