Thanks for that. I tried it out and you know what? It worked :-)
What it also showed me is that the method I was using previously actually worked, too (elliptical marquee tool - apply the same measurements for x/y in fixed size). The problem is actually with the materials I'm working with.
I've been scanning and cropping record labels (vinyl 45's) and you'd think that these are circular. Seems that they aren't. Well, the ones I've got obviously aren't!