What is the minimum tire width for a 18 mm disc rim? I have a Croix de Fer cross bike that I purchased for touring with luggage; for commuting to work, lighter touring and some mild offroad riding. While it is nowhere stated officially, I can see on this review that the rims are 18mm wide: !See the sticker What range of tire width can I run? Saint Sheldon says 25-37mm for 17mm and 28-44mm for 19mm. And that it is on the safer side. What can I ride on this rim? Also, the fact that the rims are for disc brakes and their lack of brake track makes them a tad shallower. Does that change anything to this consideration?

I think Sheldon's recommendations are a good rule of thumb - I might be wiling to go a tad narrower if I were truly compelled to do so, but that's all to be taken with a grain of salt. In terms of rim depth, it should play no part in your tire choice whatsoever as it has no bearing on how the tire will seat into the rim.