Minor varicose veins can be eliminated through a procedure called microphlebectomy. During microphlebectomy, a tiny incision is made in the skin and the varicose vein is actually removed. The procedure is done with local anesthesia and no stitches are needed. Patients are required to wear compression stockings for a few days after the procedure. microphlebectomy is associated with minimal discomfort and good results are generally immediate.