In addition to GVHD, allogeneic PBSCT has been limited by toxicity associated with conventional myeloablative preparative regimens. Although non-myeloablative regimens may reduce regimen-related toxicity, such transplants have been associated with a 30 to 40% incidence of severe acute GVHD (similar to rates observed with myeloablative regimens). Because non-myeloablative regimens appear to have reduced regimen-related toxicity, we have conducted this pilot study of Th2 cells in the setting of an immunoablative (non-myeloablative) preparative regimen.