They want to have access to a wider range of taxes and charges so that more is raised locally and less has to come from the government.
It would mean reversing the current position where councils depend on government for 75% of their funding and raise only a quarter locally.
drawing on other revenue sources such as tourist taxes, congestion charges, etc.
Why are these changes being proposed?
It has become clear that the level of council tax is reaching the limit of public acceptability.
Last year the average rise in England was 12.9% - the highest since council tax replaced the hated poll tax 11 years ago.
Pensioners and others on low or fixed incomes have been worst hit - and are making the most noise - but there are plenty of grumbles from better off householders too.
A recent report by the Audit Commission said the whole local government finance system was "fundamentally flawed", so it is not a question whether there is change, but when.
What would this mean for residents?
The LGA report echoes other studies that suggest increasing the number of property price bands council tax is based on. At the moment, the top band covers all homes worth more than £320,000. That means someone in a house worth £350,000 pays the same as someone in a mansion worth several million.
Adding more bands, particularly above the top level but also leading up to the lowest level - currently £40,000 - would make the tax more progressive.
How is central government likely to view these proposals?
A government review of council funding, chaired by the local government minister Nick Raynsford, will publish its findings on these and other options in the summer.
Ministers are being extremely cautious about change because of what happened when the Tories replaced the old rates with the poll tax.
They also know that whatever change you make you will create winners and losers - and it is the latter who will make the most noise.
When could this new system come into being?
Any major overhaul is unlikely before 2007. It makes sense to first wait for the long overdue revaluation of homes in England, which begins next year, updating the values last taken back in 1991. These new values will not be reflected in council tax bandings for another two years after that.