If you have puffy nipples, surgery can make them lie flat and flush with the surrounding skin. As part of the procedure, the areolar diameter usually shrinks about 15-20%.
You can check this out by going to my gyne website (listed below) and look in the photo gallery for puffy nipples. Check out the diameter change on patient 94 (a teen with gyne and puffy nipples). You can also check out typical results for puffy nipples, starting at patient 167.
If you are thinking about surgery, please make sure you go to an expert in gyne surgery in your area -- do your homework!
Dr Jacobs