Amid a chorus of citizens complaints, Miami-Dade commissioners approved a measure Tuesday that allows for a one-time break for residents hit with mysteriously high water bills.

The measure, sponsored by Commissioner Jose “Pepe’’ Diaz, allows the water and sewer director to reduce inexplicably high bills.

The ordinance applies only to future bills at least six times the customer’s average tab. The county already had similar relief available for customers who prove hidden leaks created a high bill.

The consumer-friendly item was part of a packed agenda in which commissioners also approved new labor contracts, shot down a proposed straw ballot on casino gambling and brainstormed about pressing the Florida Legislature for control over gambling issues in Miami-Dade County.

But the measure, which does not apply retroactively, did not go far enough to satisfy residents who were socked with huge bills in the past.

“This won’t do anything at all for me,’’ said Cynthia Potter, a South Dade resident who along with citizen activist Diane Lawrence urged the commission to make the ordinance retroactive.

In July 2010, Potter was saddled with a $6,222 water bill, nearly $6,000 above the typical $280 tab for three months service at her three-bedroom, two-bath home. After filing a lawsuit, she settled for $2,651, which she is paying off in $74-a-month installments that stretch to 2014.

“We’ll have to keep trying,’’ said Lawrence, who has been pressing county officials to act on the issue for months.

The measure, approved 10-0, would allow for cutting the excess portion of a water bill in half and eliminating any overage in sewer charges. The county estimates the move will cost $2 million in revenue a year.

Commissioner Lynda Bell had pressed her colleagues to make the measure retroactive in consideration of citizens such as Potter, but failed to win support.

In other action Tuesday, the commission voted 8-5 against a proposal by Chairman Joe Martinez to place a nonbinding straw ballot on the Jan. 31 ballot to gauge voters’ views on the hot topic of destination resort casinos in Miami-Dade. Several commissioners said it makes more sense to seek voters’ input once details of proposed projects have crystalized and the legislature has acted.

Commissioners Martinez, Jean Monestime, Javier Souto, Xavier Suarez and Bell voted in favor of the straw ballot. Voting against were Bruno Barreiro, Esteban Bovo, Diaz, Dennis Moss, Sally Heyman, Audrey Edmonson, Barbara Jordan and Rebeca Sosa.

Separately Tuesday, the commission hammered out more details of a letter the panel plans to send to the state legislature, staking its position that the county take the lead in decision-making on casino gambling. The county attorney is finalizing the letter.

Also on Tuesday, the panel approved without discussion new labor agreements for Miami-Dade Police officers and supervisors, and for aviation and general employees represented by AFSCME Local 1542.

On Dec. 19, the commission is set to take up an issue that went to impasse during contract negotiations with the Police Benevolent Association: whether officers will have to contribute an additional 5 percent toward their healthcare coverage, boosting their total contribution to 10 percent. It also will consider approving an agreement with AFSCME Local 199, if those union members ratify a tentative contract Dec. 16.