OP here: thanks *very* much chaps: very useful comments here. Having read them all, I've decided to stick with my cheap old one, which looks very like the cheaper end of things on Amazon.
With the Krups one, at first I was impressed by the expression "twin blades", but then I realised that it's simply one blade, divided in half by the shaft -- like mine! Hence, coupled with the people who said "just grind longer, if you want it finer", my decision to stick with what I've got.
HOWEVER: I have friends who, unlike this coarse-grained slurper, are definite coffee connoisseurs, but who don't yet have a grinder (they get it ground fresh at the shop). I've passed all the good advice on to them: thanks again.
John