Phlebectomy is a procedure that involves multiple small skin incisions, through which the varicose veins are removed. The number of incisions depends on the extent of varicose veins present. This procedure may be done alone, or in combination with other procedures to treat varicose veins in the legs. Depending on the size and extent of the varicose veins this procedure can be done in the office under local anesthesia or in the hospital outpatient setting with sedation.