The fat that sometimes causes the appearance of bags under the eyes lies within another compartment called the orbital septum. This fat is approached with a surgical procedure that may remove or transpose the fat to create a more youthful appearance. CoolSculpting which is non invasive non surgical fat reduction using cold therapy is currently FDA-cleared to treat the abdomen, flanks, inner and outer thighs, back bra roll , and the area under the chin. It is not approved to treat he orbital fat that can creating the bags under the eyes. At this time, there is no applicator small enough to treat such a small area. Additionally, when we consider periorbital rejuvenation, often this fat is transposed and not completely eliminated. At this time, there is no data that shows safety or efficacy in treating under the eyes, therefore I would not recommend it . It is an interesting thought though.