Several proposed future X-ray missions will require thin (≤0.5 mm thick) mirrors with precise surface figures to maintain high angular resolution (≤0.5 arcsec). To study methods of meeting these requirements, adjustable X-ray optics have been fabricated with thin-film piezoelectric actuators to perform figure correction. The fabrication and actuator performance for an adjustable X-ray mirror that forms a conical approximation to a Wolter-I telescope are reported. The individual responses of actuator cells were measured and shown to induce a figure change of 870 nm peak-to-valley on average. These measured responses were compared with predicted responses generated using a finite-element analysis algorithm. On average, the measured and predicted cell responses agreed to within 60 nm root mean square. A set of representative mirror distortions and the measured cell responses were used to simulate figure corrections and calculate the half-power diameter (HPD, single reflection at 1 keV) achieved. These simulations showed an improvement in 4.5 to 9 arcsec mirrors to 0.5 to 1.5 arcsec HPD. The disagreements between the predicted and measured cells’ performance in actuation and figure correction were attributed to a high spatial frequency metrology error and differences in mirror bonding considerations between the finite-element analysis model and the as-built mirror mount.