Also called blepharoplasty, cosmetic eyelid surgery can address sagging and loose or excess skin around the eyes both on the upper and lower eyelids. During the procedure, excess skin or fat and muscle can be removed. It is also used if you have under eye circles, puffiness due to excess fatty deposits in the eyelids, droopiness of skin under the eye, and fine lines at the outer edges of the eye. Eyelid surgery is also used to treat drooping eyelids, a medical condition called ptosis.