Every local authority will benefit from the first part of the pound;1.25 billion Scotland's Schools for the Future programme, with 14 secondaries, 20 primaries and one special school being planned.
Skills and Lifelong Learning Minister Keith Brown stressed at the Scottish Parliament's education committee that Government funding would only cover "like-for-like" replacements of old schools; local authorities with ambitions beyond that would have to dig into their own pockets.
That dismayed convener Karen Whitefield, who queried how this would allow new school designs to meet Curriculum for Excellence.
But Mr Brown insisted "we will not be delivering any building which is not for Curriculum for Excellence" and that it would be unfair to give any authority more than it needed for a like-for-like replacement in the current economic climate.
"There's no question that the current financial situation does drive down what we're able to do," he said, citing Scotland's settlement from Westminster and the rising cost of payments for completed public- private partnership building projects.
The 35 projects, and another 20 that are in the offing, will comprise a mixture of new builds and refurbishments to existing schools. It was not possible, said Mr Brown, to provide a breakdown of how many brand new schools would materialise.
The minister also expressed enthusiasm for the "non-profit distributing" (NPD) model, which brings private investors into a building project but caps their profits, with any excess going into a specially-formed local charity.
He hinted that NPD, which has been used in a few authorities, "may be more widely applicable across Scotland" and could become a prominent factor in the Scottish Futures Trust, the Government body designed to provide an alternative to public-private partnerships.