Creating a 3D / parallax effect using precomps

I'm fine with creating a parallax effect by setting layers to 3D and modifying the z-position etc... but what if all those layers are inside a pre-comp?

I've set all the layers to 3D etc... and also set the precomp itself to 3D, but then when I move the camera, the precomp looks 'flattened' and the parallax effect is lost.

There is quite a lot going on in the animation Im creating so it would be good to split certain bits into precomps... but does a parallax not work like this?