Thanks again for the tips.
I stumbled upon the Sony UX560 which is really really flat as it has a built in battery and not these "outstanding" mics. But - you cannot control the input manually, just by pre settings and I do not know if that works out for rock concerts. So I came across the Olympus LS-P1 which pretty much offers all I ask for, though it's a little thicker than the Sony, as it has a normal AAA battery used. Still a pretty tiny recorder.
Any experiences on the LS-P1 on here? (The P4 looks sexy as well, but the bluetooth is only available for Android and it has many more features than I need.)
I use Soundman mics without battery box (having the ones taking 142db, which is fairly enough for the gigs I record).
If anyone has info, I'd be grateful!