This invention provides a method for treating a subject afflicted with a hematologic malignancy comprising administering to the subject an agent targeting a hematologic malignancy-associated antigen, wherein the subject has a low peripheral cancerous cell burden. This invention also provides a method for treating a subject afflicted with a hematologic malignancy and having a high peripheral cancerous cell burden, comprising (i) medically lowering the subject's peripheral cancerous cell burden, and (ii) while the subject's peripheral cancerous cell burden is still low, administering to the subject an agent targeting a hematologic malignancy-associated antigen. Particularly envisioned are the subject methods for treating acute myeloid leukemia using an anti-CD33 antibody labeled with an alpha-emitting isotope, such as 225Ac-HuM195.