Osteogenesis imperfecta (OI) is a genetic disease for which there is currently no known cure. OI causes the osteoblasts (bone-forming cells in the body) to grow poorly, which slows the growth of children with the disease and causes their bones to bend and break easily. Some forms of osteogenesis imperfecta may cause severe disability and even death. In previous research studies performed at St. Jude, it was found that children treated with bone marrow transplant (infusion of healthy immature blood-forming cells) began to grow faster, had more minerals (material that helps make the bones strong) in their bones, and broke their bones less often than before the bone marrow transplant. Several months after the bone marrow transplant however, body growth once again began to slow down. In this research study, children with osteogenesis imperfecta will receive another infusion of bone marrow cells but without any chemotherapy. The marrow cells will come from the same bone marrow donor as their previous bone marrow transplant. It is hoped that by removing the CD3+ cells (a type of white blood cells that attack other cells that are not like themselves) from the donated bone marrow, the subject's body will be infused quite safely and that body growth and bone strength will increase. The CD3+ cells will be removed from the donor bone marrow by use of a machine called the CliniMACS System. This machine has not been approved for use in the United States by the Food and Drug Administration (FDA). The use of this device is considered experimental.