If you are older than 55 and 80 years of age or less, or are of any age with a pre-existing medical condition that prevents you from receiving high dose chemotherapy, you will receive fludarabine- cyclophosphamide-ATG-total body irradiation. You will receive cyclophosphamide as a single dose on Day -6. Fludarabine will be given once a day for 4 days in a row (Days -6 through -3). You will receive ATG on Days -4 and -3. You will also receive a single treatment of low-dose total body irradiation on Day -1. Day 0 is the day of transplantation. Rituximab may be given on Day -9 if appropriate for your disease.