Mode III is enhanced sRGB, not Adobe RGB (mode II).
If you are using Adobe RGB on your camera and display them in a sRGB color space, the colors will look dull.
I think you should set your color space on your computer the same as your camera. Use sRGB mode I (or enhanched sRGB mode III, more vivid red and greens) for web based applications or if you mainly display your pictures on a computer screen.
Use Adobe RGB mode II when you are using your files for further processing. Do not forget to set your computer working space to Adobe RGB as well!