Thing2 inherited Thing1's first helmet, which was a Netti but is the same as half a dozen other brands out there. Not too bad, but not great either.
She recently grew out of that. Thing1 got a pretty crap helmet when she grew out of it, and it really didn't sit well on Thing2 either. (Yes, it was marginally better WITH the hat)
Over the course of a few years, I've looked at quite a few kids helmets. They range from crap, to really crap. Seriously... some have a thin plastic band, adjustable, which operates as the 'cage' for the helmet. But then, the helmet itself is just Velcroed on to that. Astounding. Many one-step-up-from-the-smallest helmets I've seen have that construction.
As you may have seen, I finally got around to trying her out for a Little Nutty (well, a second time - she didn't want a bar of it at AusBike). The array of bright colours (should) make it easy to get one they'll like.
But, most importantly, the construction is great. Straps adjust well, and seem to stay put. Dial on the rear to adjust in/out. It's basically like a skate-style helmet (as are the full sized Nutcases), but with the adjustable dial on the back.
Not the cheapest helmets around (although their website -http://www.nutcasehelmets.com.au
/- does have regular run-out models) but the best I've seen. I wish I'd got one ages ago.
(I've since adjusted the straps so that it sits a little above her brow-line, and there it's sat. Very nice, and just as importantly, she loves it).