This study will determine the safety and effectiveness of a combination of the immune-suppressing drugs antithymocyte globulin (ATG) and cyclosporine for treating myelodysplasia, a disorder of low blood cell counts. It will: evaluate whether this drug combination can increase blood counts in patients and reduce their need for transfusions; compare survival of patients who respond to ATG and cyclosporine treatment with those who do not respond; and determine the side effects of the treatment.