CHICAGO (CBS) — Mayor Rahm Emanuel has come up with a way to avoid steep cuts to the city’s public library system, and it’s going to cost all city car owners.

The mayor is now proposing raising city sticker fees for all vehicles by $10 or $15 a year. Cars would pay $85, while larger SUVs would pay $135.

Emanuel said the agreement was a compromise with aldermen.

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“That is a partnership that hears what the aldermen say, listens to their suggestions and ideas and then addresses them,” Emanuel said.

Originally, Emanuel wanted to impose a steep increase on larger vehicles only. Now, everybody would have to pay more.

City clerk Susana Mendoza had cried foul over that proposed change, which she said would cost hundreds nearly 200,000 drivers an extra $60 a year. She said the city would better use its resources by going after scofflaws.

In exchange for the modification on city stickers, the mayor’s proposed library cuts would be reduced.

Some staff positions and library hours would be saved under the plan. Hours would only be cut on Mondays and Fridays when students are in school.

Non-profits will also begin to pay for a portion of their water use next year.

The announcement by the mayor came just days after a letter signed by 28 aldermen protested library and other cuts in his budget.

Simply put, the mayor said the ideas of council members were better.

Budget Committee Chair Carrie Austin called the agreement proof of a new partnership.

Other amendments to Emanuel’s budget restore Graffiti Busters and vacant lot clean-up crews.