You have to load a custom ini to your camera, but the parameters are still experimental. I tried it, bitrate changed but effect were minimal (others reported a visual improvement) and crashes if you set the bitrate too high or the if the image you are recording gets complex.
5dIII users are better of with RAW. Like its no competition. every frame is a 14-bit DNG.
Other way to get a very nice image is pregrading.
Shoot a cr2 on location. Load it in your Picturestyle Editor en begin to grade the image. Save the PS, and load it into your camera. Now you are shooting on scene with the grading you wanted on 8-bit MOVs. Saves a lot of disk space and time.