At least half of the Year 6 pupils at Sherwood Primary School in Preston, Lancashire, have attained level 5 in English. David Fann (above), the head and chair of the primary committee of the National Association of Head Teachers, hopes it might be more.
He has asked for seven of the 53 papers to be reviewed - all of them given level 4 when they are potential level 5s.
Although papers came back three days late and he has to send some back on appeal, Mr Fann counts himself as lucky.
"I am happy with our results this year, but the administration of the tests has been very poor," he said. "What upsets me is that if Sats are so important, why do children in Scotland, Northern Ireland and Wales do without them? Why aren't teachers in England trusted as much as teachers in Wales?"
The Government is trialling an alternative. The Making Good Progress pilot includes a new testing system. Pupils can sit a test twice a year and they are only tested on the level their teachers think they have reached - rather than all Year 6 pupils doing the same test at once.
But the pilot doesn't address the central issue. "The concern isn't about testing," said Mr Fann. "It's about schools targeting those children who make a difference to the league tables."