OK, it's pretty clear that "ein Paar Schuhe" is exactly two, although I'm not sure if the Neue Rechtschreibung still requires the capital P. Nevertheless, if I ask: "Gib mir doch bitte mal ein paar Zettel.", I would not expect exactly two. Three or even more, actually.
I've learned that in English, "I'll be back in a couple of hours" tends to be interpreted as "no more than two hours", whereas "I'll need a few hours longer." can definitely be more than two. I've often faced situations where my expectations were wrong when "a couple" was used.
But if I say in German "Ich brauch noch ein paar Minuten.", I think of this as more than just two.
Lately, I've seen refererences, I think on English.Stackexchange.com, where it was inferred that "ein paar" in German also means just two. Having spent the last ten years on a pacific island, I wonder if the usage of "ein paar" in German is shifting towards "just two".
 Please note that this is not about the difference between "ein Paar" and "ein paar". I'm well aware of that difference and know when to capitalise the P. I'm solely interested in the inherent meaning of "ein paar" when it is used with a lower case "p" and thus clearly NOT depicting a set "pair" of two items.
Also, "ein paar" does not cleanly translate to "several, a few, a couple". That's exactly the problem. In English, "a couple" leans very strongly towards "just two", as far as I have experienced in everyday conversation.
The purpose of this question is to establish whether or not in today's usage in German, "ein paar" is leaning towards "just two" or whether it is more likely to mean "three or more".