Chin reduction without jaw reshaping surgery?

I like the shape of my jaw bone, it seems to make a subtle V-line, especially the more I lose weight. However, I feel I have excess soft tissue on the tip of the chin bone. So much so that I can literally grab the fat on the front of my chin with my fingers without feeling bone and it doesn't go away with weight loss. I also have a bit of a cleft chin which almost seems to be caused by the fatty chin pads. What can be done? I would like to avoid jaw surgery if possible.