Relocate the top primary schools so that access to them can be more equal in the long run - this is one of the suggestions arising from a study done by two Raffles Institution (RI) alumni last year.
Another is to reduce the priority given to groups such as children of alumni as well as parent volunteers and community leaders.
These proposals arose from a study that showed that better primary schools tend to be located in more affluent estates.
The study was done by Mr Deepak Warrier, 21, who will be going to New York University next month to read economics, and Mr Pu Liang, also 21, who is studying computer science and machine learning at Carnegie Mellon University in the United States.
Mr Warrier said: "Our study started from the initial observation that many of the supposed brand-name schools are in the Bukit Timah area.
"But previous research has shown that their presence doesn't have much impact on nearby property prices - in other words, the presence of elite schools makes little difference."
The duo measured schools by the number of awards they had received from the Ministry of Education, and placed them in three clusters based on the cost of homes in their locations. The schools were given a ranking based on the number of awards they earned from 1990 to 2014.
These awards recognise academic and non-academic achievements, including school performance, teaching and administrative processes, as well as co-curricular activities.
Housing price data was gathered in July last year from the Singapore Real Estate Exchange portal, which tracks home prices.
Out of 190 primary schools, 33 were in Cluster 1, which had the highest property prices.
These schools, mostly in the Bukit Timah and East Coast areas, were on average ranked about 40 places higher than their counterparts in Clusters 2 and 3.
The next two sets of 100 and 57 schools were placed in Cluster 2 and 3, respectively, with the latter having the lowest housing prices.
Mr Warrier said there were some outliers such as Rosyth School, which was highly ranked but located in a Cluster 2 neighbourhood.
There were also some schools in Cluster 1 which were not as highly ranked but are in expensive estates.
"But the trend - that the best primary schools are concentrated in expensive estates, perhaps for historical reasons - still held overall. This creates inequities as the primary school registration system gives high priority to home-school distance," Mr Warrier noted.
"But the good news is that there is little significant difference in school quality between Clusters 2 and 3. This means that the neighbourhoods with the mid to low property prices have a range of school types.
"It's not the case that the cheapest neighbourhoods have all the lower-ranked schools," he said.
He and Mr Liang worked on the research and paper over a few months last year.
They submitted the paper to the Singapore Policy Journal in September last year, and it was published earlier this year.
The journal, which was started in 2014, is run by students at the Harvard Kennedy School. The publication invites students and researchers to write thoughtful analyses of Singapore policy.
"There are inherent inequalities in a cohort of students with different resources. Schools cannot amplify these differences," said Mr Warrier.
"In the US, for instance, public schools are funded by local property taxes - a school in a wealthy district gets more resources," he said.
"By and large, we're doing better than other countries. But we still shouldn't be magnifying inequalities by allowing children with wealthier and more well-connected parents to get into better schools," he added.
• For more information on the study: https://singaporepolicyjournal.com/2016/04/19/making-every-school-an-accessible-school