In order to accomplish these two goals, two important things will be done. Firstly, patients will get three medicines which are considered reduced intensity because they are not known to cause the serious organ damage seen with conventional chemotherapy. These medicines, however, do cause intense immune suppression so these can cause increased infections. Secondly, in addition to transplantation of bone marrow from unrelated donors, patients will also transplanted with mesenchymal stromal cells derived from the bone marrow of their parents. Mesenchymal stromal cells are adult stem cells that are normally found in the bone marrow and are thought to create the right background for the blood cells to grow. They have been shown in many animal and human studies to improve engraftment. In addition, they have a special property by which they prevent and are now even considered to treat graft versus host disease. Therefore, by using a reduced intensity chemotherapy regimen before transplant and transplanting mesenchymal stromal cells, we hope to improve engraftment while at the same time decrease the potential for severe side effects associated with a conventional transplant which uses extremely high doses of chemotherapy.