More schools are using ability banding systems or random allocation (lotteries) to select children, according to the Sutton Trust.
While main admissions criteria continue to reflect factors such as children's proximity to a school and whether their siblings attend, a growing number of institutions are using banding to provide a comprehensive intake.
The research was conducted by Professor Anne West, Dr Philip Noden and Audrey Hind at the London School of Economics. Ballots and Banding examines the admissions policies of England's 3,000 state secondary schools and academies in the 2012/13 school year.
Banding involves testing children and putting them into ability groups. The number of schools employing such a practice increased from 95 in 2008 to 121 in 2012/13. Random allocation was used by 42 institutions in 2012/13.
According to the research, the increasing popularity of banding and random allocation appears to be driven by academies and free schools, which are free to determine their own admissions policies. Some 17 per cent of academies use one or both criteria, compared with five per cent of comprehensives.
Some 155 schools now allocate places according to aptitude or ability in music, sports or other specialist subjects. The admissions code allows comprehensive schools to allocate ten per cent of their places in a specialism, while one in ten academies use this criterion.
Professor Anne West, director of the Education Research Group at the London School of Economics, said: "Banding could have the greatest effect on creating balanced intakes in areas where schools are popular and school rolls are rising.
"While banding is not a panacea, it can contribute to creating more balanced intakes than would otherwise be the case.
"The use of banding or random allocation conveys a school's commitment to providing comprehensive education and so may provide a yardstick against which the school's admissions may be assessed and reviewed."
Conor Ryan, director of research and communications at the Sutton Trust, said: "It is encouraging that more schools and academies are using banding and ballots as a way to get a more balanced intake. But it is important that in doing so they are sensitive to local circumstances."
He said more urban schools should use these methods to ensure access to the most popular comprehensives is fair.
Mr Ryan advocates the use of inner and outer catchment areas to ensure pupils living close to a school are not prevented from attending by these methods of selection.
The Sutton Trust makes a number of recommendations in the report, which it believes will help to improve social mobility through education.
It says more schools should introduce random allocation (ballots) or banding to ensure wider access to the most academically successful comprehensives. Ballots can ensure that a broad mix of pupils has the possibility of attending a school, whilst banding can ensure pupils of different abilities gain access to the school.
Cooperation between schools should take place to ensure banding is used effectively. A local admissions forum could help to achieve local coordination, with groups of schools encouraged to develop a shared approach to admissions across an area.
It also recommends employing a combination of methods to achieve a comprehensive intake. Random allocation should be used in conjunction with a catchment area or banding in order to ensure their intake reflects a wide range of abilities.
A common test should be used by schools within a particular area, so that pupils do not have to sit multiple assessments.
Government should should work with community groups, consumer agencies and businesses to make sure parents are well-informed about the education options available to them.
Mothers and fathers should be made aware of their rights to free transport to a choice of three schools within six miles of their home (or up to 15 miles for faith schools) if their child is eligible for free school meals.
David Boyle, principal of Dunraven School in Streatham, London, said banding was introduced at his institution to ensure its intake reflected the range of abilities in the local area. He said it has made it more of a community school, with 53 per cent of pupils eligible for the pupil premium.