His answer to a question in the chamber - the old one up the hill, that is, not the new one - was slowly approximating to a conclusion.
You could see Mr McConnell concluding that he had troubled the chamber long enough on the particular topic, whose details I forget. He told MSPs:  "I'm haverin' so I'll sit down." And he did.
As a statement, it struck me as perfect. Innately truthful, notably concise - and eminently inclusive, in that he cleared the floor for others to intervene.
If only, I thought at the time, more politicians would follow this admirable example. It would seem that I am not alone in sharing that view, as witness sundry noises off during the latest round of questions to the First Minister at Holyrood.
Incidentally, I say "as I recall" re the event chronicled earlier. Despite years of admittedly sporadic research, I have been unable to find those fine and noble sentiments listed in the Official Report of Parliament.
It could be, I suspect, that the Official Reporters - themselves fine and noble - regarded the former FM's comment at the time as an obiter dictum, heard in court but not legally binding nor setting a precedent.
Bear in mind that their version of proceedings, while an extremely accurate report, is not absolutely a word for word record. Many a politician, past and present, has been decidedly grateful for that fact.
Lord McConnell, to be fair, was not much given to havering; less so indeed than contemporaries. So it was particularly gallant of him to fess up.
Still, back to today. The front bench exchanges were about education. Perhaps the topic infested the discourse - but the verbiage back and forwards did seem rather longer than is regularly the case, like a weary lecturer diluting a pint of material to fill a quart pot.
Certainly, James Kelly, Labour's Parliamentary Business Manager, thought so. On a point of order at the close, he complained that exchanges involving the four party leaders had occupied twenty five minutes of the half hour allotted for questioning the FM.
What, he declared, of back benchers? At this point, you could see one or two indications of agreement from across the chamber. Mr Kelly was sounding inclusive.
But it all went agley - as such schemes, the poet tells us, often do - when Mr Kelly tried to blame the First Minister in particular for offering "speeches rather than answers". That generated a partisan rumble of discontent from the SNP ranks.
Speaking up for back benchers was one thing. Dissing Nicola was another. Up with this they would not put.
In emollient mood, the Presiding Officer Tricia Marwick said she would review the day's proceedings. (May I commend BBC Democracy Live to you, PO?)  If necessary, she would speak to Business Managers, including Kelly, J.
But earlier the PO had herself displayed eminent economy of language. Faced with an unruly chamber, she shouted:  "Wheesht!" A Scots term urging silence which I regularly deploy when herding politicians in broadcast debates.
Perhaps Ms Marwick might consider its wider use. Instead of simply demanding order, might she use a haver meter - and intervene when a front bench contribution is trying the patience even more than usual? I know, I know, inconceivable.
As to the education exchanges today, they resembled somewhat a university tutorial. Both the questions and the answers meandered more or less purposefully through extant knowledge, with much reference to established sources. There was less in the way of innovative thinking.
The task of opening the seminar fell, as it does, to Labour's Kezia Dugdale - currently a senior thane but, who knows, destined for the crown hereafter.
She tried to trap the FM with a multiple choice question on attainment, bursaries and student debt. The answers she wanted were "rubbish, down and up", in that order. Unaccountably, Nicola Sturgeon declined to follow the guide, preferring her own analysis: that things were improving but had a way to go.
There were comparable exchanges with Willie Rennie of the Lib Dems and Ruth Davidson of the Tories. In response to Ms Davidson, the FM suggested she was looking at some means of assessing progress by primary school pupils that would provide a more consistent picture across Scotland. Details, she said, to follow.
And there's more!  Those talented individuals who toil producing the Official Report at Holyrood are plainly assiduous readers of this site.  They remember Jack McConnell's comments - but reckon I got the word wrong.
They say that, rather than havering, he waffled. And they have found the report in question. It notes the former FM as saying: "My apologies, Presiding Officer, I started waffling there. I will drop it at that."
So different choice of language. But identical sentiment and impact.
Excellent. Genuinely excellent. Don't you love the by-ways of politics?
As I recall, one of the finest contributions to Scottish Parliamentary discourse came from the former First Minister Jack, now Lord, McConnell.