The main effects we will look for in this study are changes in body chemicals that are signs of bone formation or bone breakdown, and changes in bone density throughout the skeleton. We will randomly assign all study participants, who are women aged 50 and over, to either stay on alendronate alone, receive daily continuous PTH plus alendronate, or receive daily PTH for 3 months out of every 6 for a total of three separate 3-month cycles of PTH plus daily alendronate.