Coventry City council has approved plans to save £146m by 2014, which may result in up to 1,000 jobs being lost.
Threatened services include teenage pregnancy services, Consumer Direct, free swimming for the young and over 60s and the youth crime action scheme.
Staff are to be asked about voluntary redundancy and taking early retirement, but the council has warned there will be compulsory redundancies.
The authority is the biggest employer in the city, with 18,000 workers.
There are 379 managers earning more than £40,000, with some areas having 10 layers of management which the council says it wants to reduce to six.
The vote to approve the plans was 29 in favour and 24 against.
Councillor Phil Townsend (Lab) told BBC News that the authority could not be clear on the exact number of redundancies.
"It would be foolish to say it's going to be less than 10%, it would be foolish to say it's going to be more than 20%.
"We want to manage this sensitively, carefully thoughtfully.
"These are people's jobs that are going here. It will affect their lives, their ability to pay their domestic bills to care for their families.
"We are a responsible authority and we will give them every possible support we can."