The entire study is 21 months long; the active treatment period is 18 months with a 6- month followup period. The primary outcomes in this study are biochemistry and bone density throughout the skeleton. We will randomly assign all participants to either remain 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, both with PTH given in addition to daily or weekly alendronate.