Some have put in up to 80 hours of volunteer work.
Others have tried to use clan or church connections.
But despite their efforts, parents applying to 21 primary schools may still have to go through a ballot to get a place for their child.
Last night, all of these schools had more applications than vacancies - even though there was still a day to go before Phase 2B of Primary 1 registration ends.
The crunch is likely to intensify calls to review the rule giving priority to volunteers or those with school connections.
This is because some parents have complained that they are still not guaranteed a place, despite putting in the hours.
Phase 2B gives priority to children of volunteers at the school, active community leaders or members of a relevant church or clan.
CHIJ St Nicholas Girls' School in Ang Mo Kio had 30 applicants vying for 12 spots, while Fairfield Methodist School had 39 applications for 18 vacancies.
The volunteer scheme was started in 1998 to encourage parents to get to know the school better before enrolling their child.
They typically put in at least 40 hours, although some schools such as Raffles Girls' Primary have asked for 60.
Nanyang Primary, meanwhile, has raised the requirement to 80 hours - well above the Education Ministry's guideline of at least 40.
Some schools, such as South View Primary, limit the number of parents who are allowed to be volunteers to prevent balloting.
Housewife Regina Phang, 32, who has registered her child at CHIJ St Nicholas Girls' School, said: "I am on tenterhooks. Don't think I can sleep tonight."
Mr Elvin Ho has decided to look elsewhere due to stiff competition at St Andrew's Junior School, which has 58 applicants fighting for 56 places.
The 40-year-old banker had put in about 40 hours of volunteer work with his wife, from arranging and packing library books to running game stations on sports day.
But he said: "I don't think I will continue to volunteer there any more."
Despite having only seven places, Ai Tong School received 21 applications. It is one of the six schools affiliated with the Singapore Hokkien Huay Kuan.
To become clan members, parents pay $720, which covers a five-year subscription. They must also be of Fujian descent and aged over 21.
The registration crunch means fewer extra slots will trickle down to those in the later stages, who have no links to any school.
However, the Education Ministry has previously rejected calls to review Phase 2B, saying that key stakeholders - such as parent volunteers - are important as they help to strengthen the schools' tradition and ethos.