Six Charleston firefighters have filed a lawsuit alleging that the city has shortchanged them and others on overtime pay by using an unfair and convoluted system that fails to properly compensate them for the hours they work.

The collective action, filed in U.S. District Court in Charleston, alleges that the city failed to pay firefighters time-and-a-half for overtime work, in violation of the Fair Labor Standards Act.

The firefighters also allege that the city’s pay system has cheated them and their colleagues out of compensation for overtime logged during recruit school and its required training classes, the lawsuit states.

What’s more, the formula that the city used to calculate pay allegedly penalized firefighters who worked more overtime, at times dropping their per-hour rate below the legal minimum wage of $7.25 an hour, the lawsuit states.

They are seeking unspecified damages for unpaid overtime as well as attorneys fees, interest and relief, the lawsuit states.

The city has 30 days to file a formal response, and with municipal offices closed for Veterans Day, representatives from City Hall and the Fire Department could not be reached for comment Monday.

Charleston Fire Chief Karen Brack and other city officials have been working for months to restructure the pay system, which they have described as confusing and difficult to navigate. But they have not conceded to the firefighters’ claims that people are being shortchanged as a result.

Six firefighters are named in the lawsuit, but as many as 70 more have signed on to join the legal action, said their attorney, Ben Le Clercq of Mount Pleasant. The named plaintiffs are firefighters James Regan, Jesse Faircloth, Michael Pack, Thomas Haffey, Jacob Stafford and Kyle Watkins.

Le Clercq said firefighters don’t enter their profession for the money, but they deserve to be properly compensated for performing an inherently dangerous job that provides an essential service.

“They put their lives on the line every day,” he said. “It is absolutely imperative that they be paid every cent to which they are entitled under federal law, and we don’t believe that has happened here.”

Rumors of a lawsuit over the overtime dispute have swirling for months around the Fire Department. Some members of the rank-and-file contend that millions of dollars are at stake, while others have been dubious that a challenge to the pay system will result in a sizable windfall.

Brack told The Post and Courier in September that she has made it a priority to restructure the pay system. The system stems in part from a 1990s lawsuit the firefighters union filed against the city, resulting in a fluctuating workweek and a complicated formula for compensation that “is like advanced physics,” she said.

Brack has said she was in the process of finding an estimated $350,000 needed to make the shift from a salary-based system with incentive-pay enhancements to a more simple, hourly rate format.

The current fluctuating workweek system uses a mixture of base salary, incentive pay and overtime pay to calculate firefighters’ paychecks. The firefighters allege that the system has lowered their base pay on several occasions below the minimum wage.

Stafford, for example, received $1,218 after working 224 hours during one two-week pay period last year, resulting in an hourly pay rate of $5.44 — well below the minimum wage, the lawsuit states.

City Councilwoman Kathleen Wilson, chairwoman of council’s Public Safety Committee, said she wants to schedule a meeting of her panel soon to get an update from Brack on progress with the pay restructuring. Wilson said she viewed a video on the issue produced by one of the firefighters involved in the lawsuit and came away with more questions than answers.

“I am as mystified as anyone else by this,” she said. “It’s an extremely complex issue.”

Wilson said she hopes the parties on both sides of the issue will be able to sit down in a cooperative manner to come up with a more conventional method for calculating pay that is fair to all involved.

“It’s something we need to resolve,” she said. “It needs to be put to rest.”

Le Clercq’s response? “We welcome all efforts by the city to pay the firefighters time-and-a-half.”