He continues to monitor trialists, is keen on a centre-back and a centre-forward and there is interest from other clubs in "one or two" of his players. These are the routine tasks of a manager, but they also provide a refuge for McCoist. When he talks about the off-field issues at Ibrox, he has increasingly been referring to fatigue, among the fans, among the football community, perhaps even for most of those involved.
Every week tends to bring a further development on the boardroom saga at the club. Since answering back to the criticisms of Charles Green when the former chief executive returned, briefly, as a paid consultant, McCoist has maintained the stance this his business is the team and his players; what happens in the boardroom is down to the directors.
He returned to that theme yesterday, acknowledging that the continue drama at Rangers needs a conclusive ending. "Being a fan, ex-player and now manager, I just want what's best for this club," he said. "Everyone is reaching the stage where we're saying 'let's get this sorted and move on'. When I talk to Sandy [Jardine], wee Willie Henderson, big Tam Forsyth, everyone is of the same opinion: 'C'mon, let's sort this out and go forward'. If that's ex-players talking, it'll be echoed one thousand times by the supporters, but I'm optimistic that the off-the-park stuff can finally be sorted out."
It is likely to be six weeks before the club holds its annual general meeting, at which a group of disgruntled shareholders will also table five resolutions seeking significant changes in the boardroom. The accounts are due to be published in the meantime. McCoist has become well-versed in financial issues that most football managers would not expect to encounter - "it's opened my eyes to a lot of avenues I'd never have imagined I'd go down," he said - but it will be a measure of his own progress if the exploits of the team do not add to the commotion.
The season is in its infancy, but Rangers fans have taken heart from the performances of their side. The loss to Forfar Athletic in the first round of the Scottish League Cup will continue to irk them, but otherwise Rangers have shown signs of a stronger mental attitude, more variety and dynamism to their play and, crucially, a more emphatic sense of purpose. Airdrieonians were eventually swept aside last Friday night, with the kind of ruthless intent that McCoist has been demanding of his squad, and even if one game is not emblematic, the general sense is of progress.
"We've miles to go and we've had one great second-half against Airdrie, so no-one's getting carried away," said McCoist. "The squad's getting better with the players we've brought in. People have to remember we lost £40-50m worth of talent [last year] and brought in free transfers, but we're delighted with the progress we'll make this year."
Steve Simonsen, the former Dundee goalkeeper, and Sam Kelly, the 19-year-old former Everton midfielder, have extended their trial period at the club, while McCoist retains an interest in signing the Bosnian defender Boris Pandza. Negotiations are continuing between Craig Mather, the Rangers chief executive, and Pandza's agent. Several clubs are also keen on taking Scott Gallacher, the Rangers goalkeeper, on loan, with McCoist keen for the player to gain regular first-team experience.
Cammy Bell, the former Kilmarnock goalkeeper, is one of the eight players who have agreed to sign as free agents on September 1, when Rangers' registration embargo ends. He could even feature as a trialist in Saturday's match with East Fife at Ibrox, after which McCoist will be able to choose from a full squad of players. The visit of Berwick Rangers in the Ramsdens Cup tonight is not incidental, since McCoist wants to foster a hardened winning attitude within his squad. It is also an opportunity for some players to prove their worth before potential replacements are eligible to play from September 1 onwards.
"If you're Berwick Rangers, you're delighted we're not allowed to play any of our new players," McCoist said. "But I'm more looking forward to the game than having any worries because the boys that will play, those that didn't play on Friday, will know that's what expected."