As you close down your aperture on a "Canon EF 70-200mm f/2.8L IS USM Telephoto Zoom Lens" (this is not the latest version of the lens) the vignetting disappears.
The following images are a test I did photographing an evenly lit white board from f/2.8 to f/22. (Click on the first image to view larger and scroll through)
All images are the copyright of Paul D. Weinrauch and cannot be used without permission.
©2013 Paul D. Weinrauch