In 1984, the decision was made over coffee, orange juice and chocolate cake after dinner at then Finance Minister Tony Tan's home in Bukit Timah. The group settled on Mr Goh Chok Tong "fairly quickly".
In 2004, it was a powwow over a lunch hosted by then Home Affairs Minister Wong Kan Seng at the Istana. The meeting was short because "the choice was clear": Mr Lee Hsien Loong.
This time, it will not be as easy. Current and former People's Action Party (PAP) politicians say the choice of Singapore's fourth PM is not as obvious.
Mr S. Dhanabalan, a core PAP leader from the second generation who helped select Mr Goh as PM, told The Straits Times: "With this generation, there are no clear markers to say, this person should be the leader. There are a few who can do it. It is difficult to say who would be the best candidate."
Former PAP MP Inderjit Singh said: "The runway is too short and the fourth-generation leaders have not shown very clear achievements to convince their colleagues."
This will be Singapore's third change of top leadership. Mr Goh took over from founding Prime Minister Lee Kuan Yew in 1990. PM Lee succeeded Mr Goh in 2004.
Many believe the current race has narrowed to three contenders: Finance Minister Heng Swee Keat, Minister in the Prime Minister's Office Chan Chun Sing and Minister for Education (Higher Education and Skills) Ong Ye Kung. In accordance with past practices, the leader will be selected by those of his generation, to be "first among peers".
A call by Emeritus Senior Minister Goh on Sunday, for the new leader to be designated before 2018 is over, has injected a sense of urgency into the process, prompting a statement from fourth-generation ministers that they will settle on a leader "in good time".
It was signed by 16 men and women who meet regularly to discuss issues including the succession, said a party source. The Straits Times understands that as of now, no date for a gathering to settle the question has been set.
Observers say the process this time is closer to that in 1984 rather than 2004, on two fronts.
First, the discussion at which the 4G team should settle on their leader could precede the Cabinet reshuffle - which PM Lee had said would take place this year - when the person is made deputy prime minister.
In 1985, Mr Goh was made First DPM a few days after that fateful meeting. He and his team was then tasked with day-to-day running of the state, though the official handover was five years later.
Based on ESM Goh's timeframe for the current process, there is not enough time to do it the other way round, as was done in PM Lee's case, said Mr Dhanabalan. Mr Lee was made DPM 14 years before the 2004 lunch at the Istana. Three months later, he was PM.
Recalling that meal, Mr Lim Boon Heng, who was Minister in the Prime Minister's Office, told The Straits Times: "It was a short meeting because the choice was clear. As DPM under Mr Goh, Mr Lee Hsien Loong was doing a lot of heavy lifting."
During the lunch, someone put forward Mr Lee's name for PM, and "the rest of us agreed". On what the considerations were, he said: "What is important is ability, clear motivation to do what is best for Singapore and Singaporeans, not for personal glory."
A second present-day parallel to 1984 is that there is more fluidity on the question of who the leader could be.
Then Prime Minister Lee Kuan Yew favoured Dr Tan, but the latter "made it clear he would not want to be leader", said Mr Dhanabalan, describing what happened at Dr Tan's house.
"The next obvious candidate was Chok Tong. When the others said he was the best candidate, he accepted it. He was not aggressive in wanting to be the leader. He was responding to a need, rather than looking for a leadership role."
Today, whoever becomes the next PM will face a similar challenge to what Mr Goh did, said Mr Dhanabalan.
"There was a big difference in communication skills between LKY and Goh Chok Tong, but what is remarkable is that Chok Tong was able to establish excellent rapport with the public... through his own way of communicating.
"The transition from Lee Hsien Loong to the next PM will have a similar kind of gap, since Hsien Loong, in terms of eloquence, is more like his father than Chok Tong."
And so, when the next PM is identified, Singaporeans should give him the benefit of the doubt, he said, adding: "If there is any lapse in communication, they should not take it too seriously."
The years as DPM will be important in getting the public to warm up to him, just as they did to Mr Goh in the five years before he became PM, he said.
Mr Dhanabalan, who was foreign minister, revealed that he had even asked Mr Lee Kuan Yew to consider leaving Singapore for up to a year on a sabbatical with a university or think-tank during the transition period from 1985 to 1990 - to leave no room for doubt that Mr Goh was the man in charge.
The elder Lee declined. "His reason was that his wife would find it very difficult to be away from the grandchildren."
Given that today's situation seems even less clear-cut, one question is what will happen if there is a difference in opinions within the team on who their leader should be.
One way, said Mr Dhanabalan, is they could look to the present leadership to gain some indication as to who they think is a good candidate. "That will be helpful."
Veteran PAP backbencher Charles Chong said that while there may be uncertainty in the eyes of the public, "the inner circle would know much more than the public", and it would be clearer to them.
A second way is for the issue to be discussed within a broader circle of PAP MPs. Such a parliamentary caucus was introduced in 2004, when the PM-designate was confirmed by them.
Looking ahead, the next PM could have a more challenging time, given a livelier political environment, said those interviewed.
Mr Singh said he should be able to make tough decisions and shun populist policies. Mr Chong stressed intellectual ability and communication skills: "Sometimes, very good policies end up making a lot of people angry when communicated wrongly."