The study says investing in staff is more important than class size
Further reductions in primary school class sizes probably would not be good value for money, research suggests.
The study by Professor Dylan Williams of the Institute of Education in London questioned the benefit of lowering class sizes below 30 pupils.
Cutting them to 20 would cost £20,000 per class per year, he says - but would pay off only if pupils were unruly.
Otherwise the money would be more effective invested in closer monitoring of pupils' progress, says the study.
The introduction of smaller infant class sizes was a key promise of the Labour government - and the Conservative Party has spoken of the value of smaller schools.
But this study challenges the assumption that smaller classes are inherently better - saying that reducing class sizes by a third would not be the best use of resources.
Instead it suggests that investing in a more personalised tracking of pupils' progress would yield more improvements.
However the study says that small class sizes can be beneficial for infant classes - although this would need a more radical drop in numbers, down to classes of 15 pupils, suggests the study.
It also says that the success of a larger class depends on pupils being well-behaved.
"Smaller classes do confer a benefit if pupils are unruly, because fewer pupils in a class means less disruption," says the study.
"But as long as pupils are well-behaved, then what you can do with a class of 20 is generally possible with a class of 30."
The ATL teachers' union backed the findings that school staff rather than class sizes were the key to raising standards.
"We know cutting the number of pupils in a class only improves learning when there are only 15 or fewer pupils, but putting an extra professional in each classroom could have the same result," says Martin Johnson, the union's deputy general secretary.
"Schools have benefited hugely over the last decade from having more classroom based staff, but much more training is needed to make their deployment fully effective."
In England, the average infant class size is 25.6 pupils - with a legal maximum of 30 pupils.
For primary pupils between ages eight and 11, the average class size is 27.2 pupils.
A spokeswoman for England's Department for Children, Schools and Families spokesman said: "We make no apology for our focus on reducing infant class sizes and recruiting teachers - this is an important part of our strategies to help all children achieve more."
She said the Organisation for Economic Co-operation and Development had noted that the UK had increased investment in education consistently and strategically, with more money directed to attracting better qualified teachers rather than solely into lowering class sizes.