Drugs that suppress the immune system, such as sirolimus and tacrolimus, have contributed to increased success of transplantation. However, to prevent organ rejection, transplant recipients need to take immunosuppressive drugs for the rest of their lives, and these drugs make patients more susceptible to infection, endangering their health and survival. Regimens that are less toxic to or can eventually be withdrawn from transplant recipients are needed. Alemtuzumab is a monoclonal antibody that binds to and depletes excess T cells in the bone marrow of leukemia patients. This study will determine the effects of intravenous alemtuzumab and oral sirolimus and tacrolimus after kidney transplantation. The study will also evaluate this regimen's potential to allow eventual discontinuation of components of long-term immunosuppressive therapy.