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Russell Martin faces a tough competitive debut as Rangers head coach - and on Wednesday he will find out if his new side face Brann, Panathanaikos or Servette in the second qualifying round of the Champions League.
Hibernian and Dundee United will also find out their opponents as they feature in the same stage of the Europa League and Conference League respectively.
Neither Scottish champions Celtic, nor Scottish Cup winners Aberdeen, are involved at this stage.
Celtic will be seeded in the Champions League play-off draw on 4 August, when the Dons will be unseeded as they enter the Europa League at the same stage.
So what awaits Rangers, Hibs and United on Wednesday?
Martin has much to live up to in Europe after Rangers reached the Europa League quarter-finals last season under interim head coach Barry Ferguson.
However, he will hope to improve on the opening Champions League qualifying defeat by Dynamo Kyiv that meant then boss Philippe Clement's side dropped into the second-tier competition.
Rangers, as is the case for Hibs and United in their competitions, need to come through three stages this time if they are to make the Champions League proper.
Seeded for the draw, they will this time be opening their European campaign against a team who, like themselves, were runners-up in their domestic league.
On paper, Panathinaikos would provide the toughest test, the Greek side being 111th in the European club rankings, 86 places behind Rangers, with Servette 139th (one behind Heart of Midlothian) and Brann 189th.
The Athens side have never lost to Scottish opponents over 90 minutes in four meetings with Rangers, two with Motherwell and one with Aberdeen, winning four of their seven games.
However, it was Rangers who progressed when they last met the Ibrox side.
Having beaten Aberdeen 3-0 at home in the 2007-08 Uefa Cup group stage, the Greeks exiting on away goals after a 0-0 stalemate in Glasgow was followed by a 1-1 draw in Athens in the round of 32.
They had beaten Rangers 3-1 at Ibrox, and drew 1-1 at home, in the Champions League group stage in 2003, while they eased aside Motherwell 5-0 on aggregate in their latest meeting with a Scottish side in 2012 - in the Champions League third qualifying round.
Panathinaikos have not reached the Champions League proper since 2010-11 and last season started in Europa League qualifying, beating Botev Plovdiv but losing to Ajax before qualifying for the Conference League by defeating Lens.
They lost 4-1 at home to eventual winners Chelsea and beat The New Saints 2-0 in Wales in the new league stage, finishing 13th, before beating Vikingur Reykjavik in the knockout phase then losing to Fiorentina in the last 16.
The furthest Servette have progressed in the Champions League, meanwhile, is the third qualifying round, where they were beaten by Rangers after a 1-1 draw in Switzerland followed a 2-1 loss at Ibrox.
In their only other meeting with a Scottish side, they lost by a single goal to Aberdeen in the European Cup second round in 1985.
Last season, they were ousted by Chelsea in the Conference League play-off round after beating Braga.
Rangers' final potential opponents, Brann, have only once qualified for group-stage football - back in 2007 in the Uefa Cup.
Last season, the Bergen side beat Go Ahead Eagles in the Conference League second qualifying round, then defeated St Mirren 4-2 on aggregate after a 3-1 win in Norway, before losing to Astana in the play-off round.
Whichever of the three sides they face, Rangers will begin their campaign on 22/23 and 29/30 July.
Emerge victorious and they will be in the Champions League third qualifying draw on 21 July. Lose and it will be the same stage of the Europa League.
A third-placed finish has renewed Hibs' love affair with Europe, which began with two semi-finals and three other quarter-finals by 1973, but from which they divorced last season.
While Rangers have three potential opponents in the Champions League draw, there are plenty more possibilities for David Gray's Leith side.
Hibs are unseeded for the draw, with Anderlecht of Belgium, Portugal's Braga, Denmark's Midtjylland and Switzerland's Lugano among their potential opponents.
Ukraine's Shakhtar Donetsk or Finland's Ilves Tampere, Moldova's Sheriff Tiraspol or Kosovo's Prishtina, Poland's Legia Warsaw or Kazakhstan's Aktobe and Cyprus' Larnaca or Serbia's Partizan are other possibilities.
Uefa are likely to split the draw into two groups early on Wednesday morning and that would reduce the range of Hibs' potential match-ups.
Despite those heady early days of European football, Hibs have never progressed to the group stages, but they came closest two years ago.
They beat Inter Club d'Escaldes and Luzern in Conference League qualifying before being crushed 8-0 on aggregate by Aston Villa in the play-off round.
Lose this time and at least the third qualifying round of the Conference League is there as a consolation.
Memories of that 1987 Uefa Cup final are fading fast for United as they return to European football after a two-year absence after finishing fourth in the Premiership and looking to reach a group/league stage for the first time.
Having lost 7-1 on aggregate to AZ Alkmaar in the third round of Conference League qualifying last time, United will be glad that they and the Dutch side are both seeded and therefore cannot meet at this stage this season.
That is one of the few certainties in the draw, with Jim Goodwin's side having more than 60 potential opponents.
Among those, Swedish sides AIK and Hammarby might be ones United would want to avoid.
Republic of Ireland duo St Patrick's Athletic and Drogheda United, Northern Ireland's Cliftonville and Dungannon Swifts, or Welsh teams Haverfordwest County and Penybont, would be classed as easier opponents.
All will become clearer - hopefully - on Wednesday.