The board that governs the public Jackson Health System will soon shrink, following a decision Tuesday by the Miami-Dade County Commission.

The Public Health Trust will be reduced to seven members, from 17, in May. The smaller trust will be the same size as the Financial Recovery Board that has been temporarily overseeing the financially troubled Jackson system since the spring of 2011.

“The smaller number... definitely is a step in the right direction,” Marcos Lapciuc, the financial board chairman, told commissioners after they approved the change.

While Lapciuc had argued that a smaller trust would make Jackson more nimble, Martha Baker, union president of SEIU Local 1991, had opposed the reduction, in part because the nominating council that would appoint trust members would be made up of current financial board members.

But the proposal was amended to include the president of the South Florida AFL-CIO, or his or her designee, on the nominating council. The nominees will then be approved by county commissioners.

A divided commission only narrowly moved the measure forward in a preliminary vote in October. They deferred another vote scheduled for earlier this month.

But on Tuesday, without discussion, commissioners gave the plan final approval with a 7-3 vote.

Acting Chairwoman Audrey Edmonson and Commissioners Lynda Bell, Esteban “Steve” Bovo, Jean Monestime, Rebeca Sosa, Xavier Suarez and Juan C. Zapata voted in favor; Commissioners Bruno Barreiro, Sally Heyman and Barbara Jordan voted against. Commissioners Jose “Pepe” Diaz, Dennis Moss and Javier Souto were absent for the vote.

The restructuring of the Public Health Trust represents a legacy of sorts for former Commission Chairman Joe Martinez, who created the Financial Recovery Board and pushed hard to permanently reshape the trust. Martinez left office last month, after a failed bid for county mayor.

The financial board will end its term in May, and the trust will be reconvened. Heyman attempted to extend the temporary board’s term another two years, until 2015, saying Jackson could still use the additional financial oversight, but her resolution failed on Tuesday on a 7-6 vote.

In other business, commissioners decided on the county’s lobbying priorities for 2013. Key among them are several requests to tweak state election laws to prevent the long lines and slow ballot-counting that permeated last month’s presidential elections.

Among those requests: allowing counties to open early-voting sites in locations other than elections offices, city halls and public libraries, and extending the number of early-voting days to nine from eight, adding the Sunday before Election Day.

Commissioners rejected Monestime’s proposal to ask the state for 14 early-voting days — the same number Florida offered before Gov. Rick Scott signed a new elections law last year. That law reduced the number of days, while keeping the number of hours on the books the same, and eliminated voting the Sunday before Election Day, which largely Democratic, African-American churches have used as a day to bring “souls to the polls.”

The commission signed off on a resolution in September supporting the return of 14 early-voting days. But a majority sided Tuesday with Mayor Carlos Gimenez’s election advisory board, which recommended last week that Miami-Dade only ask the state to restore the Sunday-before-Election-Day voting.