After receiving stiff criticism from unions representing police and firefighters and the Civil Service Commission’s staff for its proposed overhaul of the city’s rules for classified employees, Mayor Mitch Landrieu’s administration offered several revisions to its original plan Thursday at a special meeting of the Civil Service Commission.

The changes seemed to do little to assuage critics’ complaints that the package proposed by the mayor, which still calls for ending the “rule of three” provision, would open the door to discriminatory practices and might violate the state constitution.

The “rule of three” allows department heads and hiring managers to consider only the top three eligible candidates for a promotion or an open position, based on how they score on an aptitude test.

Representatives for rank-and-file police officers and firefighters, whose unions have opposed the plan, asked the commission to hold off on considering the administration’s proposal as they attempt to work with the administration to craft a more acceptable plan.

The commission did not take any action at the meeting. The Rev. Kevin Wildes, the panel’s chairman, said another public hearing on the proposed changes would be scheduled and a vote would be at least another month away.

The mayor has proposed a package of 34 changes to the city’s civil service system. Called the “Great Place to Work Initiative,” it would give City Hall supervisors greater flexibility in hiring, evaluating, promoting and rewarding employees. It also would increase the minimum wage for city workers to $10.10 an hour.

The changes are intended, in part, to ensure that the city can hire the best applicants for available positions and retain high-performing employees, administration officials have said. But critics have argued that some of the changes would weaken the protections city employees enjoy against political influence.

Landrieu’s office presented its revised proposal to the Civil Service Commission at a special meeting Thursday. The commission’s staff, who had been critical of the administration’s first plan, did not have an opportunity to review the changes beforehand. Personnel Director Lisa Hudson said she and her staff would need time to review the latest proposals before taking a position.

The revised proposal does not include five of the originally proposed rules changes. What had been one of the more controversial items in the package, a call to eliminate the system that ranks candidates for hiring or promotion in order of their score on exams and then organizes them into bands, or tiers, for consideration, received the ax.

The city had proposed that the tiers be eliminated so that hiring managers would be free to interview anyone within the group of candidates who passed the test.

The administration also amended several other proposed rule changes, including one that appeared to shift the authority to set minimum qualifications for civil service jobs from the personnel director to a department head. The revised proposal calls for the personnel director and the department head to agree on a set of minimum qualifications and, if an agreement cannot be reached, to seek resolution before the Civil Service Commission.

The new proposal also adds a rule calling for the commission to attempt to target promotional and recruitment efforts to “attract qualified candidates who reflect the demographics of the city.”

The greatest source of division, based on Thursday’s public comment period, is a proposed change to eliminate the “rule of three” policy.

The administration restated its argument that the current rule eliminates from consideration qualified candidates who could be a better fit for a job based on characteristics other than having the highest test scores, such as additional years of experience.

But Chief Administrative Officer Andy Kopplin took his defense of the proposed rule change a step further and suggested that it would increase diversity within the ranks of the Fire Department, specifically. Kopplin said the results of a recent test for a promotion showed that on the average, minorities received lower scores than white applicants.

“The test that is used to set the ‘rule of three’ disproportionately, adversely impacted minorities in their placement,” Kopplin said. “We believe that the department should be able to review the qualifications of all those who passed the test, but those who scored at the top of the test-taking were predominantly white and those who had passing scores but were at the bottom of the distribution, they were disproportionately minority. That means the ‘rule of three,’ in limiting the selection for promotion to a smaller group than all of those who passed the test, would have disproportionately excluded minorities from getting those promotions.”

Kopplin’s comments rankled firefighters union President Nick Felton, who said Kopplin was using race-baiting tactics to try to persuade the commission to allow the rule change.

“That was absolutely insensitive. You ought to be banned from here,” Felton said. “That was absolutely uncalled for.”

He likened Kopplin’s comments to those of Donald Sterling, the disgraced owner of the Los Angeles Clippers, who was banned by the National Basketball Association and ordered to sell his team after a recording surfaced in which he made racist comments.

Felton said he intends to call for Kopplin’s resignation.

Other groups said ending the “rule of three” would encourage discriminatory hiring and promotional practices.

“We believe in the ‘rule of three,’ ” said Donovan Livaccari, a Fraternal Order of Police attorney. Together with the tiers requirement, the rule performs a “vital function for the notion of fairness and equality,” he said.

“If the goal here is to help build a workforce that more accurately reflects the makeup of the community, I would suggest that that’s best accomplished through recruiting efforts,” Livaccari said. “With regard to promotions, rules should ensure that the competitive merit system should be protected. If everyone that passes a test is equally eligible to be promoted, that is not competitive and also opens the door to discriminatory promotional practices.”

The administration also was criticized for not bringing more groups to the table as it wrote its revisions. The administration said it met with the city and state civil service departments and also consulted with an attorney to make the changes. Attorneys for the Fraternal Order of Police said they also were consulted. But firefighter representatives and the Police Association of New Orleans said the administration did not contact them.