Trapattoni's side have only let in one goal in the past nine matches, but are still hurting from World Cup play-off defeat to France.
Ireland look to erase play-off pain against Estonia
The Republic of Ireland have been here before. Not so much in Tallinn, although they did visit the Estonian capital in 2001, but in the play-offs.
For the fifth time in 14 years, they face a two-legged tie with a place at a major tournament the prize at stake.
For the second time during Giovanni Trapattoni's three-year tenure as coach, the Irish approach a pivotal situation. They know that they failed in the cruellest fashion imaginable last time. Two years ago, William Gallas's extra-time goal, with the assist coming from Thierry Henry's "Hand of Gaul", sent France to the World Cup in their stead.
"Everybody has got that scar and that wound is still there," said the defender Stephen Kelly. For two of his colleagues, however, there is another memory, of the only play-off in which Ireland prospered.
A decade ago, they defeated Iran 2-0 in Dublin and lost 1-0 in Tehran to secure a place at the 2002 World Cup.
"It seemed a bit surreal because there were a hundred thousand Iranians booing us off the pitch," said the goalkeeper Shay Given, one of the survivors.
And yet, in some ways, it seemed typically Irish. They can fare best as underdogs, a theory that is supported by a remarkable record in Trapattoni's reign: they have never lost an away competitive game. Visits to Italy, France and Russia, where Richard Dunne managed an exceptional rearguard action in September, have all produced draws.
Against the supposed minnows of Estonia, who in September achieved their highest Fifa world ranking (at No 58), the Irish are in a dangerous position: favourites. Said Trapattoni: "There is no room for complacency."
Local rivals can testify to that. Their hosts owe their place, in part, to home-and-away wins over Northern Ireland. This is the biggest game in Estonia's history. Having finished ahead of Serbia and Slovenia, both World Cup finalists, in their group, the Baltic nation intend to make Ireland their next high-profile victim.
First, however, they must breach an extraordinarily stingy defence. Ireland have let in only one goal in their past nine games. Given has been afforded remarkable protection, made all the more admirable by the raw materials at Trapattoni's disposal. Sean St Ledger, Dunne's regular partner in the centre of defence, has not even been on the bench for the Championship team Leicester for some of this season; Kelly is not Fulham's first-choice right-back while, until recently, Kevin Kilbane was the regular on the Ireland left despite dropping into League One at the end of last season.
But then, Italian managers have always had a reputation for defensive diligence. Trapattoni's tactics can seem both strength and weakness, a rigorously drilled side forever playing a version of 4-4-2 that is high on industry but low on creativity.
His unchanging attitudes, at age 72, and loyalty towards his long-serving players have generated debate. Kilbane has been jettisoned after 110 caps, but the captain Robbie Keane has retained a pivotal part in his plans despite leaving the Premier League for Major League Soccer. A record of 51 goals in 112 internationals impresses outsiders rather more than some in the Emerald Isle.
Nevertheless, with Kevin Doyle suspended and Shane Long injured, it is significant that the Los Angeles Galaxy striker, whose goal against Iran proved decisive a decade ago, made a swifter-than-expected return after being injured against Andorra last month. Either Jonathan Walters or Simon Cox is likely to partner Keane in attack.
For Ireland's veterans, this may be the final opportunity to compete in a major tournament. Their last was the 2002 World Cup when the lively front partnership of Keane and Damien Duff troubled Germany. Ten years on, they are ages 32 and 31 with more than 200 caps between them. Dunne, 32, is in a similar position. Given is 35.
Yet, for all their experience, none was even born when Trapattoni first stepped into a dugout. The elder statesman of the international game took charge of AC Milan in a caretaker capacity in May 1973. Lose over the two legs and a distinguished career may conclude.
"I don't want any more hard-luck stories," Given said, but if there are, several tales could be in their final chapter.