City Council on Wednesday unanimously approved an amended budget that implements the second phase of a compensation study for city employees and gives a 1-percent raise rather than giving a bonus.

School employees still would get a bonus, and the City Council also voted to fund a compensation study for school employees with current-year dollars.

Councilman Mike Duman proposed the amendments and said he had met with each of his colleagues individually in recent weeks.

The amendments partially reversed course from the proposed budget, which would have given only a 1.5-percent bonus to city and school employees. A raise initially was deemed unsustainable, but Duman said a variety of belt-tightening measures and improvement in the economy should cover the raises.

“I firmly believe a bonus would do little for retention and absolutely nothing for attracting new hires,” he said Wednesday.

The first phase of the compensation study was implemented in fiscal year 2013. The second phase, after Wednesday’s vote, will be implemented Jan. 1, 2015, with the 1-percent cost of living raise effective Dec. 1.

Duman said this phase of the compensation study will hike the pay of 702 city workers, with 46 percent of the monetary value going to police and fire department workers.

“I’m of the firm belief the economy is moving in the right direction,” he said after the meeting. City Council also voted to use current-year dollars to fund a third-party review of the city’s overtime pay practices, which is anticipated to save some money that can be used for the raises.

Mayor Linda T. Johnson said the plan had been vetted with the city’s financial advisers and Finance Department staff.

Each City Council member spoke in favor of the plan after Duman’s proposal.

“Everybody’s going to have to tighten up and be a little leaner, but it’s sustainable,” Councilman Roger Fawcett said.

Councilman Curtis Milteer noted that the plan should help boost morale among city workers and, indeed, the president of the International Association of Firefighters Local 2801, who spoke during late appearances, confirmed that.

“You’ve increased the morale in this city automatically tonight,” Travis Peirce said.

Several City Council members said they hope the school division also will be able to provide raises with what it’s given and reiterated that City Council does not tell the school division how to spend its money.

A 2-percent raise for teachers in the state is proposed in the General Assembly, where the budget is deadlocked over Medicaid expansion. City Council members also expressed the hope that raise will make it through the budget intact.

The city’s full budget is more than $538 million, with a general fund of $180 million. It includes no real estate tax increase.