Councils are trying to protect front-line services despite major spending cuts, according to the Local Government Association.
It said nine out of every 10 councils had reduced the cost of senior officers by cutting jobs or pay, while almost as many had cut middle management.
A survey of 131 local authorities in England also indicates two thirds are sharing services with other councils.
Unions accused the LGA of trying to put a positive spin on "disastrous" cuts.
The survey shows half of the authorities plan pay freezes to achieve savings.
Three out of every five authorities said greater savings were being made in administration, human resources, finance and information technology than in other services, although one in five said the biggest cuts would be in services for young people.
And eight out of 10 planned to target libraries for cuts.
Baroness Margaret Eaton, who chairs the LGA, said: "This survey shows just how hard councils are working to protect the services that people care about most.
"Councils know just how much value their residents place on the services they provide and are doing all they can to make sure they can continue to do so wherever possible."
She said authorities were "pulling out all the stops to minimise the impact of these cuts and build on their record of delivering new and better ways of doing things".
But Unite general secretary Len McCluskey said nobody had been "fooled" by the survey, stressing that the cuts had been a "disaster".
"The depth and scale of the government's cuts is disastrous for council services and jobs," he said. "Any attempt to put a positive spin on the situation is a bad joke."
He added: "We understand that councils have been put in an extremely difficult position and the blame lies firmly with the government. But no matter how the LGA tries to present these figures, council services are facing deep and lasting cuts."
Unison general secretary Dave Prentis said the cuts were "stripping local services back to their bare bones".
A Department for Communities and Local Government spokesman said: "Through shared services, reducing top salaries, increasing town-hall transparency and improving procurement, councils are showing that if they cut out the waste, they can do more for less and protect the front line."