Chicago Mayor Rahm Emanuel is restoring cuts to city libraries and pushing an across-the-board increase in vehicle sticker prices after a majority bloc of aldermen raised objections to some unpopular pieces of the mayor’s proposed budget.

The amendments announced Friday make up just a sliver of Emanuel’s $6.3 billion budget proposal. But it represents a concession to the 28 aldermen who sent him a letter last week outlining their concerns.

“The voters did not want Council Wars and they also did not want a City Council that would be a rubber stamp,” Emanuel said. “I think this speaks to that new partnership that I said I was gonna do in the campaign.”

The changes include restoring $3.3 million in planned cuts to the city’s libraries that will avert more than 100 layoffs. Emanuel had proposed closing libraries for four hours on Mondays and Fridays, but aldermen said that would hurt kids and people who use library resources to hunt for jobs. Emanuel’s proposal now calls for the reduced hours only while children are in school and not during summer or holiday breaks.

The mayor is also backing off a plan to hike city vehicle sticker fees for SUVs weighing more than 4,000 pounds. Now, he’s calling for an increase from $75 to $85 for cars, and from $120 to $135 for vehicles heavier than 4,500. Aldermen had been concerned that lowering the threshold for bigger vehicles would hit families too hard.

Emanuel is also delaying the hit on non-profits who will soon lose their exemption from having to pay city sewer and water fees. After aldermen cried foul about requiring small parish churches and religious groups pay for their water, the mayor is now proposing a three-year phased in discount for small non-profits, culminating in a final 20 percent discount in fees by 2014.

The mayor also said he will restore $1 million worth of cuts to city programs that clean up empty lots and graffiti.

But Emanuel didn’t seem to be giving ground on some of his other budget ideas that drew criticism from aldermen, including the privatization of some city health clinics and cuts to the city’s 911 call center.

“We have the right balance as presented in the budget, and I laid out to you the changes that I’m gonna be recommending starting Monday,” Emanuel said.

It’s unclear whether Emanuel’s concessions will be enough to assuage the concerns of aldermen and win him the 26 votes he needs to pass his budget.

But some aldermen praised Emanuel for handling budget talks differently than his predecessor, Richard M. Daley.

“To have someone to hear the concerns that we have in regards to our constituency, that’s - that’s a little different for us,” said Ald. Carrie Austin (34^th) who chairs the Budget Committee.