Why do Birds Stand on One Leg?

It's ages since I went down to the River in town - so I thought a trip might be nice. It was very pleasant with lots of butterflies and dragonflies around, and Sand Martins galore hawking low over the water. It was pretty hot, but there was a slight breeze to cool things down a touch. I spotted this juvenile Moorhen with its own private island and although they have these amazing huge prehistoric-looking feet, to see one standing on one leg seems even more astonishing. Where on earth is it hiding the other leg? And why? The answer to the latter seems to be that nobody knows. There seem to be two schools of thought. One is that they do it to conserve heat. Hardy a likely scenario in temperatures of 27 degrees, especially when standing on a pale-coloured rock. Although it could be something to do with keeping cool - so regulating its temperature. The other, which I'm more inclined towards is something to do with the bird's sleeping mechanism, possibly that half the brain sleeps along with the opposite leg, then they switch, so that one half of them is always alert to danger. This one certainly seemed to be snoozing in the afternoon sunshine.