"What are you afraid of, delegates?" asked party education spokesman Phil Willis, MP. He described the plan, under which community-based groups would be encouraged to establish trusts to run schools under contract to their local authority as "the most Liberal proposal before the conference".
Education spokesman Don Foster MP said the trusts would simply be a "reformed, enlarged and empowered governing body".
But delegates were more convinced by speakers who opposed further structural upheaval and concerns about getting people to sit on the trusts.
Peter Downes, former head of Hinchingbrooke School and a former president of the Secondary Heads Association, said he had not found any heads, governors or councillors to support the plan.
The conference approved the rest of the motion, which proposed early-years education for all 3 to 5-year-olds whose parents wanted it; a maximum average class size of 25 in primary schools and a maximum class size of 18 for foreign language courses and practical science and technology classes: the reversal of the Greenwich judgment on school admissions; and giving all children with special educational needs the right to be educated in mainstream schools.