You really are going to have to keep your gain on a tight leash - you need to make sure your getting as much output as possible from the sources going into the desk as possible.
If you own the desk it's a good idea to check into having it modded; getting it rechipped and recapped reduces the operating noise radically. Creation Audio Labs does a fantastic job with the modification and it can be done incrementally - just one or two channels at a time (or as many as you want) making it very easy to afford.
I own one and keep my input levels to the board hovering around 0 on the meter. I think it really does sound the best at 0, and the noise has never been an issue. Do you have the crappier power supply, maybe that's causing you issues?
I'm not sure what it is, because I will get noise with only a few faders up. I do have the better power supply.
And yes I will start to get some noise even with VUs at zero.
I'll try and report back with a more detailed description of the problem after the next time I go down to the studio.