Cornwall Council has been discussing possible redundancies in its Highways, Transport and Waste Department.
Councillors have been told the department has to save £1.4m from its annual budget.
Arthur Hooper, head of Operational Services, said the council hoped to make savings without too much impact on staffing levels.
The union Unison said it hoped that any losses would be spread over a period of several years.
The cuts are part of an ongoing restructuring of the county's local government after the abolition of its six former district councils and the formation of the county's unitary authority last year.
'Less than 60'
Mr Hooper said "Generally we're trying to bring together all the back office operations so that we start delivering consistent services throughout Cornwall, so a lot of the lost posts will be there. We plan to protect front line services as much as possible."
Mr Hooper added that staff consultations were under way but that he hoped that losses through compulsory redundancies would be "much less than less than 60", a figure unions said they had been told.
Stuart Roden, from Unison, said cuts were inevitable, but that he hoped all involved were keen to save jobs and services.
He said: "There will obviously be fewer jobs. It's obvious that you don't need six heads of service, six lots of accountants and six lots of reception staff, etc, etc; but it's about more than that.
"I think that we've got a common objective to protect the services that the public see; so, when they take their children down to a local park, they are getting the new playing equipment, the grass has been cut and the refuse is being collected."