The meeting, held behind closed doors, is understood to have gone to a vote, which is very rare at the regular meetings of the senior figures in the Convention of Scottish Local Authorities.
At issue was how money for the extra teachers required to boost numbers to 53,000 by 2007 and reduce class sizes would be distributed. Councils serving rural areas accepted that they were on weak ground arguing for extra money on the basis of higher school costs, since their class sizes are already much lower.
Leaders of the rural authorities therefore opted to support the status quo, in which grant support for councils is distributed on a recognised population formula. But it is understood that the two key council leaders in Scotland, Steven Purcell of Glasgow and Donald Anderson of Edinburgh, argued successfully in favour of skewing resources to the most poverty-stricken areas.
Mr Purcell, a former education convener in Glasgow, put the same "special case" arguments to the Scottish Parliament's finance committee on Tuesday, along with the leaders of West Dunbartonshire and Fife councils.
The outcome of the Cosla meeting is that councils will now hammer out the fine detail with the Executive on how the revised formula is to be applied.
The TES Scotland understands that it will be done on the basis of 80-85 per cent of grant support for new teachers being distributed on the normal population basis, with 15-20 per cent reserved for schools in the most deprived parts of the country. It is also understood there will be flexibility for authorities in the way they divert the top-sliced funds to schools.
Some education officials remain to be convinced. "Where is the evidence that throwing money at additional teachers for schools in deprived areas is going to make any difference?" one asked.
The volte-face by Cosla is significant because councils have traditionally been hostile to any ring-fencing of Government money which removes their discretion over how they spend it. But it follows strong pressure from Peter Peacock, Education Minister, who is keen to be able to demonstrate results from the Executive's drive to reduce underachievement.
Mr Peacock outlined at a conference on school leadership in September a new strategy of "progressive universalism" through which more cash would go to schools facing the greatest challenges. "We will concentrate more on those who have the biggest problems," he said.
He repeated his message at the latest in the series of TESS seminars in Inverness last Friday (page four), when he drew attention to the continuing underachievement of the lowest performing 20 per cent of pupils, the 14 per cent who were not in education, employment or training (the NEET group) and young people in the care of local authorities.