Many also say that they would like to learn at a faster pace and to be challenged more consistently.
Researchers from London university's Institute of Education asked more than 5,000 Year 9 pupils from 45 comprehensives in England whether they were satisfied with their sets for English, maths and science.
Nearly four out of 10 said they were unhappy with their sets for maths, just under a third agreed for science and a quarter for English.
While some wanted to be in less challenging groups, the majority wanted to be in higher sets: three-quarters for maths, nearly the same for science, and two-thirds for English.
Sue Hallam, who conducted the research, said large variations of ability often existed within a set, but that children tended to stay in the set they were first assigned even if their work changed.
"There are pragmatic problems with moving set," she said. "How do you deal with gaps in learning? If someone moves up, does someone else have to move down? But you need to have that flexibility."
Overall, 22 per cent of pupils said that they would like to change set in order to do harder work.
One teenager told researchers: "I feel that I am being held back from what I can achieve."
Others gave reasons that were less academic.
One pupil aspired to the middle set because "if you are in a low set you are stupid, and if you are in a high set you are a boffin".
Another said: "My friends are in that group and I would like to be able to sit next to one of them."
Professor Hallam admitted that pupils might not always be the best judge of their own ability. But she said that teachers could use interactive computer programmes to personalise their lessons for individual pupils.
"I'm sure teachers are aware that children are not all being set work at their level," she said.
"If pupils feel that their work is too easy, then maybe it is."