GIVEN they have already sanctioned a transfer spend of over £17m in this window, it may be churlish to call on the Celtic board to back Ange Postecoglou with even more cash. But here we are.
Under the stewardship of chief executive Michael Nicholson and financial director Chris McKay, the Celtic board have seemed to bury the biscuit tin mentality for good. The abandonment of a perceived overly cautious frugality has been hugely welcome for Celtic supporters, most of whom appreciate too that a level of financial restraint must however also be maintained.
But while they deserve great credit for sanctioning the permanent and expensive signings of Cameron Carter-Vickers and Jota, as well as the £3.75m capture of the promising Alexandro Bernabei and the signing of Ben Siegrist, Postecoglou needs more.
The prospect of Champions League group stage football should not only be approached as a bonus windfall, but a chance to show that Celtic can match their manager's ambitions to compete at that level.
The fortunes that participation at this stage of the competition will bring Celtic will make for a healthy balance sheet regardless of how much they eventually spend in this window, so they must invest a little bit more of that pot so that the team's points total ends up in similarly rude health as the balance sheet.
It will be a huge ask of course for Celtic as a pot four team to even finish third and secure the consolation of knockout Europa League football, so a hefty dose of realism has to be applied. But that should be the minimum aim, and Postecoglou's team is still a little short in some key positions if they are to have a fighting chance of reaching even that initial target.
That much was clear from Celtic's pre-season training camp in Austria and the Czech Republic, from both the evidence on the pitch and in the rhetoric of the manager.
Postecoglou consistently spoke of his desire to strengthen in 'two or three areas' across the 10 days of the trip, and it is known that he is referring specifically to the centre-back and defensive midfield positions as a matter of urgency for the step up in level to the Champions League.
In terms of the heart of his defence, the absence of the injured Carl Starfelt exposed the drop-off in quality there is in reserve in the position.
The Swede was training on his own while on the continent and is making good progress. His breezy workout in the hotel gym in Ostrava exhibited that, in stark contrast to the sweat-soaked, slightly hungover 40-year-old journalist who was badly toiling beside him. Just a small aside, if you struggle with your self-esteem, then exercising beside an elite athlete from Sweden is probably best avoided.
He should be back for the start of the season to slot back in beside Carter-Vickers, but with Christopher Jullien still seeking an exit route for more regular first-team football, and the highly regarded Bosun Lawal showing in the games against Rapid Vienna and Banik Ostrava that he is still a little raw for the first team, Celtic could certainly do with reinforcing that position.
Ideally, they would be able to bring in someone who can not only deputise without a stark drop-off in quality, but who is of a sufficient standard to challenge Starfelt for that spot beside Carter-Vickers on the left-hand side of the central two.
Celtic lost three goals to Rapid Vienna and two to Banik Ostrava on this tour, with Postecoglou putting the goals down to rustiness and some sloppiness in possession. It stands to reason though that defending of the sort they exhibited here would be even more ruthlessly punished in the Champions League.
Despite the embarrassment of riches Postecoglou has in midfield, it is of no surprise then to learn that he is also on the lookout for a defensive midfielder to complement the likes of Callum McGregor, Reo Hatate and Matt O'Riley, all of whom have been so impressive on the ball and in attack so far this summer.
The prevailing wisdom suggests that the only concession Postecoglou will make to his attacking philosophy in the Champions League will be to tweak his midfield set-up, putting two sitters in front of his backline.
It is a system that has worked brilliantly at times in the past, most notably in the 3-0 demolition of Rangers in February, so he needs a high-level operator to sit in there beside McGregor. Someone who can offer insurance, but who is also comfortable enough on the ball to operate within Postecoglou's system. Such players don't grow on trees, of course.
Having already missed out on Vinicius Souza, Celtic must ensure they land one of their other targets in that area, with Argentinian Fausto Vera perhaps the answer.
In fairness, Postecoglou has also consistently said he is happy with the progress the club are making in the window. For now, at least, it seems as though both dugout and boardroom are singing from the same hymn-sheet.
Deliver quality signings in these two areas, and the board may find they join the manager in being praised to the heavens by the Celtic support, and may ensure that the Celtic Park atmosphere isn't the only thing to be feared when Europe's elite come to town.