Complexes suitable for targeting and killing a human target cell comprising a first polypeptide with a binding structure for binding the complex to the cellular surface receptor CD89 (e.g. with an anti CD89 antibody) presented on the cell surface of the human target cell and a second polypeptide comprising a toxic effector domain, preferably Pseudomonas exotoxin A); to nucleic acid molecules encoding said complexes, vectors, host cells containing the nucleic acids and methods for preparation and producing such complexes; compositions and methods for using said complexes for the treatment of diseases, in particular of cancer diseases like leukemia.