The lone Welsh contenders go for broke against Zebre at the Cittadella Del Rugby in Parma on Thursday evening acutely aware that a maximum five-point win will increase the significance of Ulster's collision with defending champions Leinster at Ravenhill 24 hours later.
Successive away defeats in Glasgow and Cardiff have pushed Ireland's northern province out of the two home semi-final positions and into a fight to stay in the top four.
Their wobble either side of the traumatic European Cup exit against Saracens has given the Ospreys renewed hope that they can get to the RaboDirect PRO12 play-offs instead.
Their late setback at Scotstoun a month ago, when Tommy Seymour's try trumped Dan Biggar's trio of goals, set the Warriors off on their charge towards the top of the table.
While Ulster stumbled, the most successful of the four Welsh regions repaired some of the damage by seeing Leinster off in Swansea, then the Dragons in the Millennium Stadium double-header.
They may yet rue missing a bonus point but there is no doubt that the Ospreys are back in the equation, even if they have left themselves no margin for further error.
Nobody understands that better than arguably the best uncapped Englishman in the Welsh game, Ospreys' back row forward Joe Bearman.
"Now that we've got a chance, we have to make the most of it," says the evergreen Cornishman from Newquay.
"On the way home from Glasgow after the Warriors match, we all knew how hard it would be to get back into serious contention.
"We know what we have to do - win our two remaining games, ideally with bonus points and then hope that it turns out to be enough if Ulster drop points.
"Conditions in Italy will be hot and dry which will certainly make a change. First and foremost we have to win the game and that won't be easy. Zebre have improved to the stage where they are running a lot of good teams close but a bonus point would be a massive help."
Only three teams have managed to score four tries in Zebre's citadel this season - Munster in September, Leinster in February and Connacht a fortnight later.
Ospreys, handicapped by the long-time absence of 22-year-old wing Eli Walker, have not claimed a try-bonus on the road since they were in Galway during the first month of the season.
Bearman, part of the Ospreys' Grand Final team when they beat Leinster at the RDS in a 61-point thriller, has not given up hope of the Welsh region regaining the trophy.
"It would be a dream to reach the Grand Final again," says the flanker who qualified for Wales through residence five years ago only to miss the chance of a cap because of a groin injury.
"It was a wonderful occasion and I'd love to experience it again."
Should the Ospreys achieve their maximum-point objective in Parma, they will draw level with Ulster on points but remain in fourth place by virtue of having won one match fewer - 13 against 14.
Last year's beaten finalists at least know that they are in control of their own destiny.
A win over Leinster, whom they beat twice last season before losing the finale, would put Ulster back on course and leave the Ospreys requiring a five-pointer from their last match, home to Connacht, to have any hope of squeezing into the top four.
On the same day, at the same time, Ulster meet Munster at Thomond Park in what will almost certainly be, at the very least, a fight for third place.
It could conceivably be a duel for second place should the Warriors fail to extend their storming finish to seven wins on the spin.
Like the Ospreys, Glasgow's finest are in Italy this week, at Treviso on Friday evening. After record-breaking crowds at Scotstoun for their last two home matches, the Warriors know that two more wins will secure them the glittering prize of a home semi-final.
If head coach Gregor Townsend needs any evidence that Treviso can be the trickiest of fixtures, he need only remind his players what happened when Munster went there last September.
The European Cup semi-finalists succumbed 29-19, undone by two tries from Italy wing Ludovico Nitoglia and seven goals from the New Zealander, Mat (repeat Mat) Berquist.
Stand by, then, for a momentous RaboDirect PRO12 weekend - starting with the Ospreys on Thursday and finishing with Munster on Saturday, back at Murrayfield where Edinburgh beat them 29-23 in the European Cup last autumn.
Remaining fixtures:
Leinster: v Ulster (away, Friday), Edinburgh (home, May 10)
Warriors: v Treviso (away, Friday), Zebre (home, May 10)
Munster: v Edinburgh (away, Saturday), Ulster (home, May 10).
Ulster: v Leinster (home, Friday), Munster (away, May 10).
Ospreys: v Zebre (away, Thursday), Connacht (home, May 10).
Top four finishers in previous seasons:
2012-3: 1 Ulster (81 pts), 2 Leinster (78), 3 Warriors (76), 4 Scarlets (66). Grand Final: Leinster 24, Ulster 18.
2011-2: 1 Leinster (81 pts), 2 Ospreys (71), 3 Munster (67), 4 Warriors (65). Grand Final: Ospreys 31, Leinster 30.
2010-1: 1 Munster (83 pts), 2 Leinster (70), 3 Ulster (67), 4 Ospreys (63). Grand Final: Munster 19, Leinster 9.
2009-10: 1 Leinster (55 pts), 2 Ospreys (52), 3 Warriors (51), 4 Munster (45). Grand Final: Ospreys 17, Leinster 12.
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