We report on the fabrication and performance of (1-x) Pb(Zn(1/3)Nb(2/3))O3-xPbTiO3 (PZN-PT) single-crystal relaxor piezoactuators with interdigitated electrodes patterned on a single surface. An electric field gradient across the sample thickness induces a differential contraction between opposite faces, and it is responsible for the actuation. The samples are poled by energizing the electrodes at 100 degrees C and cooling in a field. Calculations of the piezoelectric response based on a periodically modulated dipolar field yield good agreement with experiment. Discrepancies with the model are ascribed to multidomain formation in the ferroelectric sample as a result of field reversals in the applied electric field along the sample length.