This 2-year study will test the effectiveness of combining parathyroid hormone (PTH) and alendronate for treating osteoporosis in postmenopausal women. Alendronate is a drug used to treat osteoporosis and primarily prevents bone loss, whereas PTH increases bone formation. We will treat the study participants either with PTH and alendronate, alendronate alone, or PTH alone. We will determine the effects of these treatments by looking for changes in bone mineral density in the hip and spine.