Griff, if you were getting virtually no carbs, you'd be in a state of kitosis, correct? Which I'm really not interested in entering. Also, veggies not only have vitamins and minerals, but phytochemicals and those "antioxidants" that everybody is crazy over..
Jess: I'm in ketosis pretty much 24/7 these days. Remember that ketosis is not just the burning of stored body fat, it's the burning of dietary fat as well. Ketosis just means using fat for energy (instead of using carbohydrates for energy). Since about 70-80% of my daily intake is fat, that's where a lot of the ketosis is probably happening - which is not to say that I don't still burn a lot of body fat too, since my current caloric requirements per day far exceed the 1200-2200 calories I generally take in.
I can give the phytochemicals a miss, and most of those antioxidants are either a vitamin or a mineral already anyway. Avoiding carbs, for me, is far more important, and I can get the stuff I do need by taking supplements and avoiding the carbs.