At 3.30 p.m. on every Tuesday when the Dail sits, a meeting vital to the Government's survival is held in the office of the Chief Whip, Mr Seamus Brennan.
With Mr Brennan are the three Independents supporting the Government: Mr Jackie Healy-Rae, Kerry South; Mr Harry Blaney, Donegal North East; and Ms Mildred Fox, Wicklow.
The week's business is discussed and any problems the TDs might have are ironed out. Nothing is left to chance in ensuring their support in crucial divisions.
The Taoiseach, Mr Ahern, made it clear to his Ministers early on that he wanted the three Independents facilitated at all times, conscious that in the unpredictable world of politics a government can be toppled by a breakdown in communication or sheer disorganisation.
A Minister told The Irish Times: "Bertie lived through the nightmare of the collapse of the FF-Labour government under Albert Reynolds. Then he came within a whisker of becoming Taoiseach and lost it.
"He is determined that this Government will last and that he does not go down in history as somebody who held the office for a very short time and then blew it."
The three have access to all Ministers and, if necessary, to Mr Ahern. A civil servant in the Department of the Taoiseach has been assigned responsibility for them, and they can call him directly with queries, requests or complaints.
Their powerful status has led the Mayo Fine Gael TD, Mr Michael Ring, in a lively Dail speech, to describe Mr Healy-Rae as "the real Taoiseach" and Ms Fox as the "real Tanaiste".
What they require most relates to routine constituency work, be it a delay in a headage payment, the allocation of road grants, a place on a hospital waiting list and so on. Their constituency representations get priority and they may speak directly to the Minister.
Mr Healy-Rae, for instance, is sometimes an early morning caller to the Kildare Street office of the Minister for Agriculture and Food, Mr Walsh, with a long list of representations passed on by his farming constituents.
The colourful Kerry South TD, who broke with Fianna Fail after failing to get a nomination to contest the general election, is perceived to have done particularly well, having been given the chairmanship of the Oireachtas Environment Committee on Mr Ahern's instructions.
The three Independents will not be kept "on side" by the smooth processing of constituency work alone, however. Late last year, Ms Fox forced the Government to change its position on the funding of the Louth residents' group in its legal action against Sellafield. When all three expressed their concern about the proposal in the Finance Bill to tax some credit union deposits, the Government quickly got the message and abandoned it.
They keep in contact and take soundings from each other on their support for the Government when controversial national issues arise.
Mr Healy-Rae and Mr Blaney know each other since they both worked in Fianna Fail by-elections in the 1960s. Although she is of a different generation, they have a good working relationship with Ms Fox, supporting her stand against the Government on Sellafield.
All three are reported to have written agreements with Mr Ahern, but none will disclose their detail.
Mr Healy-Rae's, in particular, has assumed the mystery and intrigue of the Third Secret of Fatima, but he will say no more than give the occasional tantalising hint to the public and the media.
Mr Ahern is equally tight-lipped. Challenged by the Kerry North Labour TD, Mr Dick Spring, in a written Dail question, to place copies of the agreements in the library of the House, the Taoiseach replied: "I do not propose to add anything further to the record of the House, or to place various copies of correspondence in the Dail library.
"What I wish to reiterate, for the record, Ceann Comhairle, is that it is the intention of the Government to deal with most of the issues raised by the deputies in question during the life of this Government. We plan to do this within the parameters of departmental expenditure estimates."