The review panel, which keeps a watching brief on the way HMI inspects authorities, states in its latest report: "Headteachers are clearly an important provider of evidence and HMIE should consider more formalised methods for scoping their views."
Poor reactions by headteachers to the leadership and management of their authority, such as in Fife and East Dunbartonshire, have generally led to an adverse report and a clear-out at the top.
The panel, which meets at least once a year under the chairmanship of Mike Ewart, head of the Scottish Executive Education Department, has concluded that authorities as well as headteachers, teachers, parents and pupils "remain widely positive and supportive of the (inspection) process and are now looking for small refinements."
The panel agreed with HMI that, as well as refining the way in which heads are consulted, parents and young people should become more involved, particularly as the second round of inspections moves on to scrutinise children's services and child protection issues.
Analysis of the 27 HMI reports on education authorities up until June shows that 31 per cent of judgments on the various quality indicators were very good, 43 per cent good, 22 per cent fair and 4 per cent unsatisfactory.
Of the seven authorities that were inspected last year, four were judged to have very good performance in most or almost all aspects of their work while three turned in only a fair performance in a majority of aspects.