This is a randomized, prospective, open-label study in which osteoporotic postmenopausal women self-administer synthetic hPTH-(1-34), alendronate, or both, every day for 2.5 years. Participants initially come to Massachusetts General Hospital once a month, and subsequently once every 3-6 months, for measurements of serum and urine indices of bone formation and resorption, serum and urine toxicity tests, and DXA/QCT measurements of bone mass. One-third of the participants take hPTH-(1-34) daily, one-third take alendronate once daily, and one-third take both daily (Phase A, months 0-30).