Council tax is set to rise by 4.2% across England and Wales, according to a study commissioned by the BBC.
The government had threatened to cap the spending of councils
Local authorities will raise bills by £53 to £1,302 for an average band D property in 2007/08, it found.
The rise is the third lowest annual increase since the tax began in 1993, but is still above the Consumer Prices Index inflation rate of 2.7%.
The survey, for BBC Radio 4's Today programme, covered two-thirds of English and Welsh councils.
Steve Freer, of the Chartered Institute of Public Finance and Accountancy, which conducted the survey, said a government threat to cap spending if increases went above 5% had "concentrated minds".
He added: "This will be regarded as a very positive result in Whitehall and in town halls up and down the country.
"The second lowest annual increase in council taxes for 13 years is a significant achievement."
"Councils simply do not want to set a collision course with government with all of the uncertainty and risk which that involves."
He said the 4.2% increase is slightly higher than some recent predictions.
The results will be seen by the government as a victory for their strategy of threatening to cap local authority spending if council tax and budget requirements increase by more than 5% and 6% respectively.
But Lib Dem local government spokesman Andrew Stunell said the rise would be too much for some.
"It will be a heavy blow for pensioners and people on low pay," he said.
"The council tax is getting increasingly unfair and when it rises above the rate of pay inflation and even more above the rate of pension inflation that clearly puts people in great difficulty."
The average council tax increase for 2006/07 was 4.5%.
The campaign group IsItFair, which calls for the reform of council tax, said another above-inflation rise will anger people on low and fixed incomes, such as pensioners.