In a rebuke to Mayor Carlos Gimenez, Miami-Dade commissioners on Tuesday rejected his administration’s recommendation for awarding a contentious baggage-wrapping contract at Miami International Airport, choosing the second-place bidder instead.

A veto-proof majority of commissioners chose to hire Safe Wrap, which held the coveted concession for nine years until 2010, over TrueStar USA, the county-owned airport’s current vendor.

During nearly four hours of political wrangling from the dais, Safe Wrap matched TrueStar’s offer to pay the county a $9.6 million minimum annual fee. But the baggage-wrap concessionaire pays either that fee or a percentage of its monthly gross revenues, whichever is higher. Safe Wrap did not agree to match TrueStar’s 65 percent, sticking to the 52 percent offered in its second-place bid.

In months with heavy passenger traffic at MIA, the percentage of monthly gross revenues from encasing luggage in clingy plastic to prevent theft has exceeded the minimum required payment owed to the airport, Gimenez told reporters after the vote.

“This means that there will be less money,” the mayor said. “I’m not happy about that.”

Commissioners, however, were fine with the result. They said they lacked confidence in the generous projections from TrueStar, a corporate venture between the airport’s current vendor, Sinapsis Trading USA, and its Italian parent, TrueStar Group SpA.

A year ago, commissioners reluctantly reduced Sinapsis’ minimum payment to the county to $8.7 million from $11.1 million. The company said it could not uphold its commitment in part because competitor Secure Wrap of Miami began wrapping bags at locations outside the airport. Secure Wrap and Safe Bag USA, a subsidiary of Italian firm Safe Bag Italia SRL, joined forces to form the Safe Wrap corporate venture.

“I don’t want anyone to come back to us in a year and say, ‘I can’t pay what I promised,’ ” Chairwoman Rebeca Sosa said.

Commissioners also cited findings of a county audit completed in December that, among other things, recommended that Sinapsis keep a better paper trail of its sales and provide all of its financial records in English. Some were kept in Italian and Spanish.

Safe Wrap, whose bid received a higher score on technical merits but lost on price, had protested after being bested by TrueStar. A hearing examiner upheld the county’s TrueStar recommendation last month, requiring a two-thirds majority vote to overturn it.

Commissioners voted 9-2 to reject Gimenez’s recommendation. Sosa, Vice Chairwoman Lynda Bell and Commissioners Esteban “Steve” Bovo, Jose “Pepe” Diaz, Audrey Edmonson, Barbara Jordan, Dennis Moss, Javier Souto and Juan C. Zapata voted for the rejection. Commissioners Jean Monestime and Xavier Suarez voted against. Commissioners Bruno Barreiro and Sally Heyman were absent.

After the rejection, commissioners voted 11-0 to award the contract to Safe Wrap, which agreed to cap per-bag wrapping fees at current Sinapsis rates. TrueStar had asked for the ability to charge $20 for small bags instead of the $15 it currently charges.

“Every time that you increase the price for the customer, you’re going to lose a share of the business,” a jubilant Safe Wrap President Radames Villalon said after the vote. He said the company might try to bring its business wrapping baggage outside MIA back into the airport.