Many thanks to you all for your kind and helpful comments! 
Paul, I had thought about rebating (for which I might also use some square or even narrow, flat section), but would still prefer the piece to be slightly less in your face than the 10 x 10 mm which is the smallest one I could find at the DIY shop.
ChrisB,
That does indeed look as though it might do the trick! As I only need a short piece (+/- 1" ) it shouldn't be too tricky to grind off the uneeded sides …
well, we'll see … but thanks, once more, for all your help!
/Mattias
Edited By Banjoman on 02/02/2016 08:14:22