The city and the New Orleans firefighters union reached a compromise today on a longstanding compensation issue, with the city agreeing to provide firefighters years of back pay for hours they worked filling in for their superiors.

The cost of the back pay hasn’t been totaled yet because no one has determined who’s eligible.

In an interview after the meeting, First Deputy Mayor and Chief Administrative Officer Andy Kopplin said those details will be worked out in a legal settlement as early as the end of this week.

The New Orleans Civil Service Commission on Monday unanimously approved a change to the city’s Civil Service Rules that will require higher rates of pay for Fire Department employees who take on the additional responsibilities, provided the work lasts at least 12 hours. Under some circumstances such as fires, firefighters designated as “primary operators” while filling in for higher-paid employees will immediately qualify for the higher pay. City law requires the New Orleans City Council to approve the changes to pay.

The Fire Department will adopt an internal policy in the near future fully detailing what kinds of events will trigger the waiver of the 12-hour minimum. The pay bumps will range between 10 percent and 28 percent.

The commission also resolved the stickier issue of whether to hand over back pay to firefighters who have previously worked above their pay grades, and how far back it should apply. Officials in Mitch Landrieu’s administration, previously resistant to back pay, agreed to it dating to late 2013, when the firefighters union first brought the issue to the Civil Service Commission’s attention.

Eligibility for back pay will be based on a different policy than the one passed today, which applies to future pay.

Union President Nick Felton was not satisfied with the administration’s offer. He said back pay should go back to 2010.

In offering his objection, Felton alleged a pattern of retaliation “from the second floor” of City Hall, home to the mayor’s offices, toward firefighters over this and a number of other disputes. Firefighters are also seeking tens of millions of dollars in unpaid pension contributions and required raises.

He pointed to an incident on Friday in which firefighters were brought in to assist the cleanup of a homeless encampment under the Pontchartrain Expressway. The operation came a few days after firefighters staged a mock funeral procession near City Hall to draw attention to the firefighters who have died while waiting for back pay they were owed.

Felton said firefighters were forced to clean up human waste even though the work is not part of their normal job requirements. In an interview, Felton said that removing firefighters from their companies to deal with the cleanup unnecessarily diminished the department’s ability to fight fires.

In an interview after the meeting, Deputy Mayor of External Affairs Emily Arata denied Felton’s allegations of retaliation.

“The Fire Department has participated in numerous cleanups under the expressway of the homeless camps there. Biohazardous response is part of their duty,” Arata said. “The allegation that this was some sort of retaliation is offensive and untrue.”

Commissioners said Monday’s meeting was not the appropriate time for the argument and voted to accept the administration’s back-pay offer.

“Whatever the date is, it’s dollars that’s going into somebody’s pocket,”  Commissioner Ron McClain said. Addressing Felton, he added, “You got an offer on the table with the alternative of taking everything off the table. Nick, you got a bird in the hand.”

It’s not clear what Monday’s compromise will cost.

A March report by the Civil Service Department staff found nearly 7,000 instances of firefighters stepping up to work in higher-ranked positions in 2012 and 2013. Department staff members estimated paying for those hours could cost the city hundreds of thousands of dollars.

Kopplin told the commission that the city has not yet prepared a report on its fiscal impact. Kopplin said the City Attorney’s Office might have a draft settlement ready by the end of this week.

While the 12-hour standard won’t apply retroactively, “The people who would have been compensated in the past, had the rule we adopted today been in place, are in fact the same people who will get compensated under the agreement,” Kopplin said in an interview.

But the rule applying to back pay under the agreement is stricter than the new rule. In order to qualify, firefighters will have had to work at a higher pay class for at least five full days in a calendar year, rather than 12 hours. And the position they were covering for had to have been budgeted by the city but left vacant.