A preparation of T-lymphocytes transduced with a lentiviral vector expressing a compound chimeric antigen receptor (cCAR) containing two distinct units of CARs, one specific for the CD123 (interleukin-3 receptor alpha chain or IL3RA) antigen and one specific for the CD33 antigen, with potential immunomodulating and antineoplastic activities. Upon administration, the CD123-CD33 cCAR T cells specifically and simultaneously target and bind to tumor cells expressing CD123 and/or CD33. This induces selective toxicity in tumor cells that express the CD123 antigen and/or the CD33 antigen. CD123 is normally expressed on committed blood progenitor cells in the bone marrow; its overexpression is associated with increased leukemic cell proliferation and aggressiveness. CD33 is expressed on normal non-pluripotent hematopoietic stem cells and is overexpressed on myeloid leukemia cells. Targeting two different antigens may improve coverage and protect against antigen escape and relapse as it is less likely for tumor cells to lose both antigens. Additionally, the CD123-CD33 cCAR T cells express CD52 on the cell surface. This allows the depletion of the CD123-CD33 cCAR T cells with the administration of the anti-CD52 monoclonal antibody alemtuzumab, in case of unacceptable side effects.