You might try taking lecithin for cellulite. It dissolves fatty tissue.
In fact, Iodine and fatty acids need each other. In Dr. David Derry's book, he says that one of the important function of Iodine is to bind softly to fatty acids to transport and protect them to the various places in the body.
Lecithin has both Omega-6 & Omega-3 as well as the phosphatides.
Flechas told someone (sorry no quick reference here) not to expect Iodine to correct a particular thyroid problem (auto-immune?) -- but to use phosphatidyl choline (lecithin) and betaine. I'm sure he meant in addition to iodine.
In other words, iodne and fatty acids work together and it's very important to get them both. And, you need a balance of those fatty acids. (I like lecithin, sunflower seeds and a little flax.)