The Headteachers' Association of Scotland plans to press the Scottish Executive to carry out a national consultation on other indicators that could define more accurately the nature of a school.
The Association of Directors of Education in Scotland and the Educational Institute of Scotland supported the move, saying they too felt that free meal entitlement (FME) did not give a sufficiently rounded picture.
A spokeswoman for the Executive said there were currently no plans to consult on changing the measurement of deprivation in school rolls.
However, she revealed that the inspectorate has been working on a pilot scheme since 2003 to use other measures as well as FME when benchmarking one school's attainment against another. HMIE will be reporting its findings on this study to the Executive "in due course", she said.
Since inspectors are already using many of the same indicators the HAS is proposing, many will interpret this as a sign of tacit official approval for change. Among the measures used by HMIE to benchmark schools'
attainment are: mothers' educational qualifications, records of needs and individual educational programmes (IEPs), and attendance.
Lindsay Roy, the HAS's president, who has been spearheading the association's stance on FME, proposes that these and measures such as referrals to a children's panel and the percentage of pupils requiring special arrangements for sitting exams would be better indicators.
"We have been looking at FME for some considerable time as a proxy indicator of deprivation," Mr Roy commented. "While I understand why it has been used, I think the time is right to look at a more sophisticated indicator to gauge the flavour of a school's catchment."
Some of the information from the national census, such as family size and economic classification, might be useful, he said, even if it might be outdated.
"The more indicators you have the less impact each one will have unless some are given a higher weighting than others," Mr Roy said. "My prime purpose is to get a more accurate reflection of what a school catchment area is like.
"If FME is the sole indicator, schools with distinctly different catchments, such as very rural and highly urban, are grouped together, when in reality it is difficult to make a true comparison between them. In some cases you are comparing apples with oranges."
Where a school is seen to have lower attainment than another with similar FME, local authorities sometimes employ what are commonly termed "support and challenge" tactics.
The HAS's sister organisation in England, the Secondary Heads Association (SHA), shares its concerns about the use of FME as a single measure of deprivation and has called for prior attainment at primary school to be included when evaluating a secondary school's "value added" impact on pupils.
Roy Jobson, president of the ADES and director of the children and families department at Edinburgh City Council, said his authority has been using indices of multiple deprivation. "When unemployment rates were high and you got high rates of FME, the figures tended to be more reliable indicators, but there has been a difference recently because of the big reduction in unemployment," Mr Jobson said.
"People who are just moving into work are coming off benefit. There isn't a big difference in income and social need, but they are being taken out of social need so the figures are less reliable," Edinburgh now included other socio-economic figures such as housing benefit, clothing grants, other data relating to housing, children's panel referrals and the percentage of parents who have been through higher education.
"I have a lot of sympathy with what Lindsay Roy is saying. As an authority we are operating with exactly that model," Mr Jobson said.