Participants will randomly receive either ATG or Daclizumab. If they are in the group to receive ATG, they will be admitted as inpatients to undergo the first 10 to 14 days of treatment. If they do not already have a catheter in one of the large veins of the neck, chest, or arm, one will be placed. ATG will be given through the catheter. Blood counts and other blood analysis will be monitored daily while the patients are treated. After about 10 days, they will be released, to be under the care of their referring physicians. Those participants who are in the group to receive Daclizumab will receive a total of five doses, one every 2 weeks, over 8 weeks, given through a vein as a 15-minute infusion. The first, third, and fifth dose will be given at the outpatient clinic. The second and fourth doses can be given either at the clinic or by the patients' primary hematologists.