This study investigates the effectiveness of parathyroid hormone (PTH) in combination with alendronate, a standard treatment for osteoporosis that blocks or reduces bone loss. We are using alendronate because it may help protect patients against any possible harmful effects of PTH in cortical bone such as the long bones or hip. We are testing two different treatment schedules of PTH-one in which we give PTH daily and one in which we give PTH for 3 out of every 6 months in a cyclical fashion. The entire study is 21 months long; the active treatment period is 18 months with a 6-month followup period.