Blepharoplasty, also referred to as eyelid lift, is a surgical procedure designed to correct drooping upper eyelids and baggy skin below the eyes by removing excess fat and skin. If vision is impaired due to the droopy eyelid skin, your insurance company may cover the cost of this surgery. Often eyelid surgery is done in conjunction with other cosmetic procedures such as a facelift. Eyelid surgery is usually done under i.v. sedation.