The purpose of this study is to look at whether the combination of lower-dose chemotherapy with two chemotherapy (anti-cancer) drugs, called busulfan and melphalan, and an antibody medication called alemtuzumab (Campath®), can prevent rejection of donor blood stem cells so that those cells take hold and build a healthy new blood cell factory after transplant. The study will also look at the safety of the combination of drugs and of the transplant of peripheral blood stem cells from a healthy relative or an unrelated donor.

Transplantation of related or unrelated allogeneic peripheral blood stem cells (PBSCs) after administration of a reduced-intensity regimen of busulfan, melphalan and alemtuzumab will be associated with satisfactory engraftment and acceptable post-transplant non-relapse mortality.

Inclusion Criteria:

• Age 50 to 75 years or age 18 to 49 with one or more of these risk factors: prior autologous, allogeneic or syngeneic HCT (Hematopoietic cell transplantation); not in first complete remission or first chronic phase; and/or presence of one or more medical conditions that would place the subject at high risk such as heart and kidney disease.
• Subjects with hematologic cancers must have received at least one previous course of chemotherapy or biological therapy. In other words, the subject cannot enroll in this trial for initial treatment of the disease.
• Availability of a healthy related or unrelated volunteer allogeneic donor.

Exclusion Criteria:

• Eligible for another study or standard of care treatment that offers higher probability of cure or long-term control of subject's disease.
• Severe abnormal function of organs such as heart, kidneys, liver.
• Untreated or progressive central nervous system involvement by the disease.
• Subject is pregnant or breast-feeding.
• Performance score is below 50: at the least, requires considerable assistance and frequent medical care.
• Positive for the HIV [AIDS] virus
• Life expectancy less than 12 weeks with conventional treatments.
• For subjects capable of having children, refusal to practice birth control while on this study and for at least 12 months after PBSCT or after stopping post-transplant immunosuppressive treatments, whichever occurs later.