z-index not working with fixed positioning

I have a div with default positioning (i.e. position:static) and a div with a fixed position.

If I set the z-indexes of the elements, it seems impossible to make the fixed element go behind the static element.

#over {
  width: 600px;
  z-index: 10;
}

#under {
  position: fixed;
  top: 5px;
  width: 420px;
  left: 20px;
  border: 1px solid;
  height: 10%;
  background: #fff;
  z-index: 1;
}

<div id="over">
  Hello Hello HelloHelloHelloHelloHello Hello Hello Hello Hello Hello Hello Hello Hello Hello Hello
</div>

<div id="under"></div>

Or on jsfiddle here: http://jsfiddle.net/mhFxf/

I can work around this by using position:absolute on the static element, but can anyone tell me why this is happening?

(There seems to be a similar question to this one, (Fixed Positioning breaking z-index) but it doesn't have a satisfactory answer, hence I am asking this here with my example code)