At fringe meetings last week, the Education and Employment Secretary kept saying that Labour's pledge to abolish the Assisted Places Scheme and pump the savings into primary staffing would in fact produce one teacher per eight primary schools. "A butcher's cleaver seems to be the way forward," she said.
Labour has said it would use the money liberated by abolishing the scheme (costing Pounds 118 million in the current year) to bring all infant classes below 30 pupils. But initial savings from phasing out the scheme would be small (perhaps Pounds 20m in the first year). And, Mrs Shephard remarked, the party did not seem to have thought out what would happen if one pupil was added to a class of 30.
"Would they add a whole extra teacher when the class got to 31?" she asked journalists, adding, with a Gallic shrug, "mystere".
For Mrs Shephard, abolition of the APS is just one sign of Labour's opposition to selection and choice. She underlined the Government's support for the scheme last week by announcing its extension to private primary schools. But for independent schools, it is the vital issue on which they hope to focus public attention in the run-up to the next General Election.
First signs of this appeared during the Tory party conference last week, when full-page advertisements appeared in the Guardian and The Times aimed at changing Labour and Liberal Democrat plans to scrap the scheme. Featuring a two-faced image of Harriet Harman, Labour's social security spokeswoman, the advertisement includes contrasting quotes from Ms Harman. The one on the left opposes selection and backs the abolition of the Assisted Places Scheme and the one on the right supports parents' right to choose. "We agree with the Harriet Harman on the right," it says.
The advertisements were paid for by the Friends of Independent Schools (FIS), an association of parents and other supporters of independent schools which is run from the London offices of the Independent Schools Information Service (ISIS), the main promotional body for private schools.
Leading figures in the independent sector are feeling disgruntled that, after two years of talking to Labour politicians about the scheme, they have got no further than assurances that a Labour government would not stop LEAs buying places at independent schools.
Labour politicians have been discussing with independent school heads ways in which they could develop links with local state schools to justify the subsidy they receive through their charitable status.
Although Labour now says only that it is keeping the schools' charitable status under review - earlier pledges to remove it have been abandoned - independent schools still worry that a Labour government might undermine them in several ways.
But it is the ending of the Assisted Places Scheme that most concerns them. And independent schools believe that Labour's policy is a vote-loser. A MORI poll conducted in August for ISIS found that more than half (55 per cent) of the people intending to vote Labour at the next general election supported assisted places, and the figure was even higher (64 per cent) among Liberal Democrats.
Labour, however, cannot afford to abandon or water down one of its few cast-iron pledges on education - and one where the party is not open to embarrassment. While the party's leader sends his son to a grant-maintained school and the social security spokeswoman sends hers to a grammar school, no leading Labour figure has yet been caught with a child on an assisted place.