Abstract: Provided are methods and compositions conditioning a patient for an allogeneic transplantation, wherein the patient's hematopoietic stem cells (HSCs) are depleted with an HSC-depleting composition and the patient is then administered allogeneic cells selected from bone marrow cells, umbilical cord blood cells, hematopoietic stem and progenitor cells (HSPCs), peripheral blood CD34+ cells, and peripheral blood CD34+ and CD90+ cells; optionally the patient is also administered a medicament selected from the group consisting of a T-cell depleting or inhibiting antibody or antibody fragment, NK-cell depleting or inhibiting antibody or antibody fragment, immunosuppressive drug, and any combination thereof. The HSC-depleting composition comprises a compound selected from the group consisting of: an antibody or antibody fragment with specific binding affinity to a protein displayed at the HSC surface, a conjugate comprising an HSC-recognition molecule and a toxin, and any combination thereof.