The argument against Leeds United's chances of winning the European Cup continues to disintegrate into dust after an agonisingly tense night here in La Coruna brought them to their first place in the semi-finals for 26 years.
Whether their nerves will have recovered in time for the last four clash with another Spanish outfit in Valencia is another matter. This was a torrid evening and Deportivo will reflect they had the chances not only to extend Leeds to extra time but to have concluded the most astonishing of comebacks.
In the end, however, the damage inflicted upon the Spanish champions at Elland Road proved to be irretrievable, Leeds winning the numbers game thanks to their 3-0 triumph in west Yorkshire 13 days earlier. Mission accomplished, but only just.
Javier Irureta, the Deportivo coach, had argued that "miracles can happen in football" and, for all the splendour of Leeds's first-leg advantage, the Spaniards' imperious home form dictated that O'Leary's side would have to banish the evils of complacency if they were to dispose of la Liga's champions.
Of the previous 31 teams to visit Estadio Riazor over the last 15 months, only Milan had left the Galicia coastline with a victory to their name. Moreover, it was little more than a month ago, O'Leary had tirelessly drummed into his players, that Paris St Germain plundered a 3-0 lead here before capitulating to four headed goals in the space of 27 minutes.
Leeds, however, were surely made of stronger stuff. Since their demoralising introduction to the Champions League at the hands of Barcelona last September they have acclimatised to the vertiginous surroundings of Europe's premier competition like old hands rather than raw novices, afraid of nothing and no one.
That was just as well for this was never going to be an occasion for the faint-hearted. It was inconceivable that a side of Deportivo's credentials would be as pallid as they had been at Elland Road a fortnight ago, but Leeds could scarcely have expected the opening exchanges to have been so nauseatingly uncomfortable.
After only nine minutes they were trailing. Harry Kewell was culpable of a slight push on Victor as he tracked him back into the penalty area and the Italian referee Stefano Braschi awarded the home side a penalty. Brazilian striker Djalminha stroked his penalty expertly into the left hand corner of Nigel Martyn's goal.
Alan Smith could, perhaps should, have levelled when he latched on to a weak backpass and rounded the goalkeeper Francisco Molina only to hit the side-netting.
If Leeds thought they had repelled the onslaught, they were sorely mistaken. Instead they will reflect upon Martyn's brilliance in tipping Romero's rasping drive on to the crossbar five minutes after the break and thank their lucky stars that Deportivo's finishing did not match the exquisite nature of their build-up play.
The pressure was unremitting and after Roy Makaay had directed a header against the woodwork in the 70th minute the hosts' overwhelming superiority was finally rewarded for a second time.
O'Leary will have been perturbed by the loose marking as Valeron worked his way down the left and when he centred the ball for his fellow substitute Tristan the striker tucked his shot beyond Martyn from eight yards out.
That sparked the most ferocious of late rallies but Leeds held on and their first ever campaign at this level is threatening to become one of the truly great stories.
Deportivo La Coruna: Molina, Manuel Pablo, Romero, Noureddine Naybet, Mauro Silva, Djalminha (Valeron 69), Fran, Pandiani (Turu Flores 79), Victor (Tristan 62), Donato, Makaay. Subs Not Used: Songo'o, Cesar, Scaloni, Fernando. Goals: Djalminha 9 pen, Tristan 73.
Leeds United: Martyn, Mills, Ferdinand, Matteo, Harte, Bowyer, Dacourt, Batty, Kewell (Bakke 77), Smith, Viduka. Subs Not Used: Robinson, Wilcox, Burns, Maybury. Booked: Ferdinand, Martyn.
Referee: Stefano Braschi (Prato).