They do not come bigger than the current French champions Toulouse, and when Connacht run out on the Sportsground on Saturday, there is much at stake - not least the need to get back to winning ways.
Win and Connacht still have a chance to qualify for the quarter-finals; lose and Connacht can concentrate solely on resurrecting their PRO14 season after a disappointing return from the festive interprovincials.
Those Christmas failures account for half of the six losses Connacht has suffered since losing to Leinster 11-42 at the Sportsground two months ago. In between there have been hard-fought wins over European colleagues Montpellier and Gloucester at home (both by three points ), and a 12-point victory over the visiting Southern Kings. They have not been convincing wins, but they have demonstrated a growing resilience in Andy Friend's squad - character that will be needed in bucketloads when the swashbuckling French side face Connacht for the eighth time in European fare.
The Irish province has won just two of those fixtures - the famous victory in France six years ago and another in 2016/17 - so they know it can be done. And this is the ideal occasion, in front of an expected sell-out crowd, to show they are better - a hell of a lot better - than their last game, and to rubber stamp they belong in this competition.
Everybody involved in Connacht Rugby craves a win, and all agree it will require a fully focused performance, one of true grit, the ability to overcome any on-field mistakes immediately by regaining composure, because this is a game that may not possibly define a season, but it will prove a mark of progression - mentally as much as physically.
"We know what the equation is, we want to get that win," says Friend. "We are back at the Sportsground, we want to be winning in front of our home crowd, so it's a very important game for us for many, many reasons."
A significant boost is the return of some 10 players. Both World Cup players Bundee Aki and Jack Carty are free to play after their two-week required rest; captain Jarrad Butler and fellow Aussie backrow Colby Fainga'a are declared fit; prop Finlay Bealham and Peter Robb are available after undergoing HIA protocols in the Ulster loss; Ultan Dillane can make a return having been rested last week; while Matt Healy, John Porch, and Rory Burke are also available.
"It's a good spot to be in," agrees Friend after a tough and attritional festive period. "You need to have your stronger and most experienced players out there, so there is some really good quality and experience coming in."
Both Carty and Aki have "bounced back" after their break
"We saw when Carty came back, and a lot of the players from the World Cup, that it had been a really tough campaign for those men. I thought Jack's last 20 minutes against Munster was fantastic. He said before that he didn't feel fatigued, but he went away on that break and halfway through I'm getting a text, saying 'didn't realise how tired I was', but he's doing great now, and has bounced back in here with Bundee full of energy.
"They can't wait to get out there, and I can't wait to watch the pair of them to be honest because when they have that energy back that you see in their eyes, they are pretty special for us. Jack was one of the shining lights last year for us and he was rewarded with the green jersey, so he knows how to get back there.
After last weekend's hefty defeat to Leinster, Friend believes Toulouse, "in a weird way" is exactly what Connacht need.
"We knew it was always going to be a period when we were going to be stretched, and we have been. Now we have Toulouse and it's a chance to show what we have, and it's really important to perform. We haven't had the performance or the result we wanted in the last three weeks, but we have 80 minutes coming up against a quality side, so we know we have to be on our game. That is our target, and the focus is on our performance."
There are still some selection headaches, no doubt, and if Friend follows form, he may reward a couple of youngsters who put their hand up in Connacht's second-half showing against Leinster. Scrumhalf Kieran Marmion is back training, but unlikely this week, and with Caolan Blade in need of a rest, will Andy Friend opt to bring in Stephen Kerins or Angus Lloyd? Peter Robb comes into contention to join Aki in midfield, while options on the wings include John Porch, who has been passed fit, Matt Healy, Kyle Godwin and Niyi Adeolokun.
Up front Tom McCartney, who took a leading role for Connacht in the second half against Leinster, is expected to return to the front row, alongside Paddy McAllister and Finlay Bealham, also returning from injury.
Gavin Thornbury - one of the league's top line-out poachers is expected to line out - as is Ultan Dillane, while Joe Maksymiw looked in fine fettle when sprung from the bench against Leinster. In the back row Friend's backrow options have also been considerably boosted. Friend may rest Eoghan Masterson, who has seen a lot of football this season, but Paul Boyle, captain Jarrad Butler and Colby Fainga'a are also available. And reports that French side Lyon are looking to sign Colby Fainga'a have come as no surprise to Friend, who says "any club worth its salt would be looking at Colby".
Whichever XV are selected, Friend will be expecting a different performance than that against Leinster. No one can deny Leinster's credentials - brilliant to watch and playing a superbly confident and well oiled display - but Connacht will be disappointed with their inability to get their hands on the ball in the first half, lacking dynamism.