If you are getting very obvious vignetting (I.e. it looks like your image is framed by a blacked out circle) I am willing to bet you have Auto DX Crop off in your shooting menu.
Under image size in your shooting menu turn it on and it will automatically put your D600 in DX crop mode when a DX lens is on it. In the VF you will see a box around the image that will be captured (as it is smaller than the FX image area).
In DX crop mode your 11-16 shouldn't vignette that badly at all.