Patients with beta-thalassemia (Cooley's Anemia) continue to suffer from the transfusion-induced iron overload due to the inadequacies of current iron-chelation therapy. Compliance with the use of the only FDA-approved drug for removing excess iron from patients (Desferal) continues to be a major problem despite convincing evidence that it markedly reduces morbidity and prolongs life. The full potential of iron-chelation therapy will not be realized until an orally-effective drug is available. This small trial is testing the premise that a combination of drugs as a new approach to iron chelation therapy may reduce side effects and increase efficacy. If both drugs can be given orally, there may be a better chance of finding a suitable alternative to Desferal. Several combinations of experimental iron chelating drugs are being used in this trial.