Strange DX Crop on D600

DX lenses used in FX mode will vignette MOST (always some) at smaller apertures. Try wide open, but if that is a kit lens wide open may be 4.5 or 5.6 depending on the focal length you choose.

Play around and see what happens. I am able to use my DX 35mm1.8 up to 2.8 on the D600 in FX mode, and after all, you can always factor the vignetting into your framing and crop it out. This lens gives me a decently wide low light interior lens, as I have the kit 24-85mm, and it is NOT a fast lens.