This study will evaluate the effect of pamidronate a drug that decreases bone resorption (breakdown) on osteogenesis imperfecta. This is a genetic disorder of collagen, the major protein in bone. The abnormal collagen causes weak bones, and children with severe osteogenesis imperfecta sustain many fractures throughout their lives. They also have growth deficiency, curvature of the spine, crumbling teeth, hearing loss, easy bruising and heart and lung problems. The study will compare bone density, quality and strength, final adult height, trunk height, and functional ability in children who receive 1) pamidronate every 3 months, 2) pamidronate every 3 months + growth hormone injections, 3) pamidronate every 6 months, or 4) pamidronate every 6 months + growth hormone injections.