Efforts by Serco, the private firm running Bradford's education service, to lower the targets in its contract have forced councillors to seek legal advice.
Their move comes as an independent schools chief said tough targets on raising children's attainment by 2011 should stay.
Serco signed a ten-year contract with Bradford Council in July 2001.
It was selected for the prestige job - the biggest and potentially most profitable education contract in the country - after agreeing to meet the very high targets set by Bradford.
The Council was forced to turn to the private sector after a harsh Ofsted report found it was not up to the job of running an LEA itself. But after a year of public/private partnership, Serco failed to meet 47 out of 52 targets and now wants to renegotiate its contract.
It missed out on profits of up to £870,000 in its first year, collecting only £8,450 in performance-related bonuses. Classroom standards in poor-performing Bradford did rise, but not far enough to hit targets set in the contract.
Councillors are now taking legal advice to find out if they are obliged to re-open talks with Serco.
"Council members are taking a very firm line and believe that a contract is a contract, that's the view of members of all political parties," said Councillor David Ward, executive member for education. He added that legal advice was being sought to clarify the Council's position.
David Mallen, the independent chairman of Bradford Education Policy Partnership, said he would not object to tweaking the short-term targets if Ofsted - who will report back on Bradford in a fortnight's time - believes they are too high.
But he is against changing the longer-term ones. "My own judgement is that the ones for the first few years are too ambitious," he said.
"I would be opposed to any lowering of the long-term targets. They are also ambitious but realisable. I can accept that change takes time to effect, but our aim must remain that we transform Bradford schools as quickly as possible."
There is little sympathy for Serco among teaching unions, which have always opposed the privatising of the service.
Ian Murch, of the Bradford branch of the National Union of Teachers, said: "Very high targets were set to justify privatisation which was supposed to be able to deliver things that a conventional LEA could not. As everyone knew really, this was not going to happen."
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