Education Secretary Charles Clarke announced the changes to the specialist school programme this week, including the creation of new specialisms in music and humanities.
He explained he had dropped the advanced label after headteachers complained that it would discourage collaboration.
Much will remain from the advanced schools programme, which has attracted more than 300 bids. Specialist schools will still be able to bid for an extra pound;60,000 per year if they can demonstrate they are strong performers in their specialism and do not already receive a leadership incentive grant.
The project will now be called the Leading Edge Programme, and it will be open to schools who want to make joint bids and also to independent schools.
Fee-paying schools will have to show they are willing to work closely with state schools. Mr Clarke said: "I believe there are independent schools which have something to contribute, and we want to encourage collaboration."
He added that the Department for Education and Skills was investigating the idea of giving beacon status to individual departments in schools.
Plans to reward independent schools were praised by the Secondary Heads Association. But Doug McAvoy, general secretary of the National Union of Teachers, said that giving private schools pound;60,000 was a gross waste of tax-payers' money. "It assumes that independent schools can teach state schools a thing or two," he said. "A glance at last year's exam results shows that independent schools have a lot to learn from their colleagues in the state sector."
Mr Clarke also announced the creation of two new specialisms: music, and humanities, which can include English, history and geography.
In addition, schools can attach "minors" to their titles, becoming specialists in such areas as English and citizenship or history and classical civilisation.
Schools in rural areas may add a "rural" specialism which would include studies relating to agricultural and the local community.
Letters, 25 New Specialist System is available at www.teachernet.gov.ukmakingadiff