There was a increase in the number of families appealing against their allotted primary school place in England for 2005-06, figures show.
Applications increasingly are made electronically
Official statistics show 14,930 appeals were heard by an independent panel compared with 13,600 a year earlier. Of those heard, 36.1% succeeded.
However, they represented fewer than two in every 100 new admissions to maintained primary schools.
Secondary school appeals fell by 9% to 41,650. Parents won 36.4% of them.
So overall there was a small decline, welcomed by Schools Minister Jim Knight.
"We already know most children get a place at their first choice school and today's figures show that the vast majority of parents are satisfied with the schools their children are admitted to.
"I share every parent's desire to get their child into the school they want - young people deserve no less."
He said: "We are determined that every young person has fair and equal opportunity of getting a place in their preferred school.
"It's our absolute priority to make that process transparent and easily understandable."
Liberal Democrat education spokeswoman Sarah Teather said that behind the numbers were thousands of worried parents struggling to get the best for their children.
"If every parent in an area wants their child to attend the 'good' school, there simply won't be enough places for every child," she said.
"This cannot be realistically described as 'choice'.
"Until every school is a good school the concept of school choice will be meaningless."
The head of the Association of Teachers and Lecturers, Mary Bousted, said: "Although only one in 20 parents appeal against a secondary school place, this represents just the tip of the iceberg when it comes to parents' annual anguish over the admissions process.
"The government has misled parents in pretending they have choice, when the most they are entitled to is the right to express a preference.
"Parents should be spared the agony of choosing a school when, in reality, research shows schools differ little in their effectiveness."