Education Minister Peter Peacock has said he wants headteachers to be given more powers, allowing them to make their own decisions.
Headteachers hope to have more say in how their schools are run
His words were met with a round of applause by secondary heads at their annual conference in Edinburgh.
International research indicates that schools do improve if headteachers have reasonable autonomy.
However, the Headteachers' Association Scotland (HAS) said it wanted local authorities to continue to play a role.
Scottish headteachers would be likely to have more control over staffing and spending although they would not have as much independence as their English counterparts.
The BBC has discovered how much say on spending local councils currently give to heads.
The worst offenders are Clackmannanshire, Fife and Highland which devolve less than 60% of education spending to headteachers.
East Lothian, Eilean Siar, Inverclyde, Orkney, Moray and the Scottish Borders also gave their headteachers less independence.
South Ayrshire Council gives its heads most control, at more than 90%.
It is followed by East Ayrshire and East Renfrewshire.
North Lanarkshire, West Lothian, Stirling, Edinburgh, Glasgow, East Dunbartonshire, Perth & Kinross and North Ayrshire also fared better than the Scottish average.