Councils say they are on top of monitoring schools and have a proven track record of moving on headteachers or senior managers who are not up to it and replacing them - sometimes temporarily - by experienced colleagues.
Few heads or directors now survive a mauling from HMI with most offered early retirement or a sideways move. Last year's HMI report on Scottish schools suggested that leadership was fair or unsatisfactory in 15 per cent of primaries and 20 per cent of secondaries - in other words, well below standard.
The Education Minister last week raised the spectre of English-style "hit squads" if the recent raft of improvement measures do not lead to higher standards, particularly in literacy and numeracy. In her response to the national debate, Ms Jamieson said she would not be afraid to send in other managers.
She warned that if authorities were unable to drive up attainment she would consider "greater powers of direction". Ms Jamieson said it was unlikely private organisations would be involved, as south of the border, but pledged to bring in others within Scottish education.
"These would be people in some of the very good local authorities, which are delivering, and which could provide the kind of leadership and support that is needed. I would expect local authorities to ensure that they are dealing with underachievement or a failure to improve," she said.
However, her tough remarks have been dismissed by education directors.
Bruce Robertson, Highland's director, said councils already had powers under the Standards in Scotland's Schools 2000 Act, easier dismissal procedures and the new competence standards to tackle underachievement. By working closely with HMI, they would address any school issues.
"If an authority wants to take extreme measures, the power is there already," Mr Robertson says.
Highland, for example, recently changed the head of the small, island primary in Eigg after a particularly poor inspection report with seven unsatisfactory verdicts, including leadership.
Mr Robertson admitted: "We have had the powers to address leadership issues but there are some instances where local authorities should have been prepared to use these powers in the past."
In Aberdeenshire, Hamish Vernal, education director, said: "I think we have more than robust arrangements for quality assurance and are prepared to take wider action if necessary."
In the past, Doug Marr, former head at Banchory Academy, and then one of the country's most prominent school managers, was drafted into Fraserburgh Academy for six months. The authority has acted similarly in primary.
Mr Vernal said the normal approach was a school action plan, backed by anything from additional resources to better buildings and equipment. Extra staffing was sometimes the answer or curriculum support through an adviser.
Short-term secondments are another option and "very rarely we remove staff altogether".
Fiona McLeod, head of quality assurance in Edinburgh, said the authority operated a "support and challenge" agenda through link officers who monitor schools' progress on attainment, development planning and self-evaluation.
A headteacher is attached to the education support service to offer particular advice and support.
Mrs McLeod said: "We would also put a mentor in, another headteacher to work alongside them. From time to time, an acting head would be taken from another school."
The city's schools are now on the second cycle of a six-year rolling programme of review, based on standards and quality reports. "Every review is published and reported publicly," she said.
In East Renfrewshire, there is a system of support and counselling for teachers and heads who are "not hitting the targets that we think they should hit". For heads, that would be leadership, for teachers it could be classroom performance or "any aspect of the job in which they are not coming up to standard".
Support could be another head sent in to work alongside and if that does not work, it is the "disciplinary route". More than one head has been taken out and allocated administrative duties.
East Ayrshire tells a similar tale with support packages offered to teachers and heads who have not come out of inspections well. The approach has been "effective".