The invention provides a Pseudomonas exotoxin A (PE) comprising an amino acid sequence having a substitution of one or more B-cell and/or T-cell epitopes. The invention further provides related chimeric molecules, as well as related nucleic acids, recombinant expression vectors, host cells, populations of cells, and pharmaceutical compositions. Methods of treating or preventing cancer in a mammal, methods of inhibiting the growth of a target cell, methods of producing the PE, and methods of producing the chimeric molecule are further provided by the invention.