Patients who require a second transplant to achieve the required amount of islets will return for the procedure when a compatible organ is donated. The second procedure will be done as described above. As before, insulin will be infused for 24 hours following surgery. It will then be stopped, however, and will not be resumed unless blood glucose levels reach above 180 milligrams/deciliter. Patients will continue taking FK506 and rapamycin indefinitely. Daclizumab will be given every 2 weeks for 4 doses following the second transplant, and then stopped. Patients will take an antiviral called ganciclovir for 14 weeks and another antibiotic for 1 year following surgery. For the first year after surgery, patients will have frequent blood tests to monitor drug levels and immune function. They will return to NIH for a complete history and physical examination 2 and 3 years after the final islet transplant and will be contacted yearly by phone to ascertain their general health status and whether they remain insulin independent.