If you agree to take part in this study, and if you are one of the first 40 patients, you will be randomly assigned (as in the flip of a coin) to 1 of 2 groups. You or your physician will not know the results of this randomization. If you are in Group 1, you will have a non-radiated white blood cell transfusion. If you are in Group 2, you will have a standard white blood cell transfusion (with radiation). If you are less than 50 years old, you will receive 4 transfusions of radiated white cells. If you continue to show signs and symptoms of infection you will receive additional white cell transfusions based on the group you were randomized to.