For the study, all patients will receive a test dose of 1 mg of alemtuzumab infused into a vein during the course of 1 hour. If the dose is tolerated, the medication will be given at 10 mg doses into the vein for 10 days, as an infusion of 2 hours. Blood samples of 2 tablespoons will be taken daily, and vital signs will be measured daily. The ECHO and 24-hour Holter monitoring will be repeated after patients receive the last dose of the medication. Because suppression of the immune system results from a decrease in white cells that fight infections, patients will take medications to protect them against infections and to treat them if infections occur. If needed, patients will receive blood transfusions for their MDS. Side effects of alemtuzumab involve a temporarily significant lowering of the number of red blood cells, white cells, and platelets. Side effects of the infusion can be rigidity, or stiffness, and fever, as well as risks of infections resulting from the decrease of white blood cells. Blood counts and reactions to all procedures will be carefully monitored throughout the study. After patients receive the last dose of alemtuzumab, they will have follow-up by their referring doctor or at NIH. They must be able to return to NIH after 1 month, 3 months, 6 months, and annually for 5 years after the study. At follow-up visits, there will be blood tests to reevaluate blood counts and test for the presence of viruses. Blood tests will be done weekly for the first 3 months after patients have completed taking alemtuzumab, every other week until 6 months, and then annually for 5 years. There will also be a repeat ECHO at the 3-month visit, and a repeat bone marrow biopsy at the 5-month and 12-month follow-up visits, and as needed after that.