Councillors voted behind closed doors last night to pay more than £2 million extra to the company operating the district's highways maintenance contract.
The Executive Committee went into private session yesterday to discuss an extra payment to Atmos, which won the £8 million contract in 2001.
The extra costs will be found from the transportation, planning and maintenance budget.
Councillors have been told they will break the authority's code of conduct if they discuss the financial details.
But a source outside the Council has told the Telegraph & Argus of the amount under discussion and said it involved extra costs claimed to have been incurred by the company.
The committee was advised by the Council's director of legal and democratic services Gerry Danby that the item should be dealt without the press and public being present because the report contained information which was exempt under both the legal and financial parts of the Local Government Act.
But leader of the Labour group Councillor Ian Greenwood moved the item should be held in public, saying the Council Tax payers of Bradford had a right to know how millions of pounds of their money was being spent.
And he added it was an "outrage" he was being gagged by a warning that he would break the code of conduct if he let the public know what was going on.
The contract is due to end in April when the Council changes the system and takes on some of the work itself.
After the meeting, executive member for the environment Councillor Anne Hawksworth (Con, Ilkley) gave a statement saying: "It was agreed we would pay Atmos for work which had been done."
Coun Hawksworth said she could not name the amount because it would break the terms of the National Code of Conduct to discuss it.
Coun Greenwood said at the meeting: "This report could have been prepared without these details. It could have been written in a way which made it clear what the expenditure and the provision were. It is effectively a gagging order. It means I can't speak about expenditure totalling millions of pounds."
He said today his group had voted against the payment at the meeting.
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