Suspending clothes rail

pledgeX

I've just bought a sliding clothes rail (this one), but I'm having a bit of a dilemma working out how to fix it.

I want to fix it to the ceiling, but the cupboard I'm putting it in has a substantial lip on the top edge (about 3 inches tall) meaning the rail needs to be fixed about 3 inches lower than the ceiling in order to allow it to slide out.

Any suggestions on the best way to fix it? I could just pack it out with a decent chunk of wood, but that'll be fairly heavy, and once the rail if loaded with clothes that's going to be heavy too.

Couple of pics in case it helps:

brightontraveller

Add timber noggins to frame work the support would then be from the framework supported from ground assuming existing frame works 2x2 or bigger it should be fine looking from top down wall I=I wall, side on I-I