As Peter said, with my new convection oven I tried par-baking the crust (covered with foil) as an experiment and found the results to be superior. Haven't tried it yet with the gas oven, but I will. I know Giordano's and Connie's don't par-bake, but others might for the sake of time and expediency. It certainly won't hurt, so give it a try.
Usually I make plain cheese deep dish, but if I'm going to add veggies (especially wet ones like green peppers or mushrooms), I've found it best to saute them in a little oil, or just with a bit of water (less calories!). As far as I know, Giordano's does not saute. In my convection oven, I have made thin crust with raw green peppers, onions, and mushrooms with no problem at all with excess liquid. I will try it with deep dish when I can!