Alesse is a really low dose pill. Levlen (levora, nordette, portia) have exactly the same hormone as alesse, just with a little bit higher dose of both (30mcg ethinyl estradiol, 0.15 mg levonorgestrel) which should prevent breakthrough bleeding.

Other options: Usually switching to a triphasic pill will decrease the late breakthrough bleeding (OTC, OTC lo, cyclessa) or switching to a pill will a higher progestin (Mircette(kariva), Microgestin 1/20(junel 1/20, Loestrin 1/20 have the same amount of estrogen as alesse).