The Scottish Executive was prepared to fund more than the 20 bids selected this week to be the first "schools of ambition", but the others on the shortleet were not sufficiently "ambitious".
A spokeswoman for the Executive said: "We did not have an upper limit but expected at least 20. Had the other schools met the criteria and the required standard, we could have involved more schools."
She said officials would work with the remaining schools on the original shortleet of 43. The Executive is also inviting applications for the next round of bids.
The spokeswoman said: "This is a new programme, and people don't know what we are looking for. Hopefully, the 20 schools chosen will act as trail-blazers to show the others what they can do."
It was felt that some schools had difficulty articulating their ambitions in writing, but when the selection panel visited them their strengths were more apparent. The panel has representatives from HMIE, the Hunter Foundation, education authorities, the Executive and teacher organisations.
Over the next few months, successful schools will be matched with potential philanthropic partners, although some of the those selected already have strong private sector links.
Peter Peacock, Education Minister, said: "It's not just about private sector money, but about getting peoples' interest in bringing about change."
Many of the schools appear to have commended themselves because they have new headteachers, which often follows a poor HMIE report.
Local authorities and heads have welcomed the Executive's decision not to focus on "failing" schools. Instead, the first tranche is a mix of high-performers, those that need to improve following poor inspection reports and those that recognise they can move their performance up several gears.
Jack McConnell, First Minister, said the schools chosen "have demonstrated the vision and drive to transform themselves, to realise their own potential and to get the best for every child".
Mr Peacock stressed that there were structural differences between the Scottish template for schools of ambition and city academies in England.
"We are not so interested in the capital side, but in the change process," he said.
The Education Minister declared firmly that there was no intention of adopting the practice in England of giving private sponsors a bigger say over the curriculum and management. "What we have is right for Scotland and it is up to people in the south to do what they think is right."