Osteoporosis, a condition in which bones are fragile and break easily, is a major health problem for postmenopausal women. Research studies have shown that both estrogen/progestin replacement therapy (hormone replacement therapy, or HRT) and alendronate are effective in preventing and treating osteoporosis. However, because these drugs work in somewhat different ways, a combination of the two drugs might protect women from osteoporosis better than either drug alone. In this study we will test whether HRT and alendronate given together for 3.5 years to postmenopausal women with low bone mass will have a greater effect on bone than either HRT or alendronate given alone. We will also give every participant in this study calcium and vitamin D supplements.