We present a piezo-driven translatable mirror with excellent pointing stability, capable of driving at frequencies up to tens of kilohertz. Our system uses a tripod of piezo actuators with independently controllable drive voltages, where the ratios of the individual drive voltages are tuned to minimize residual tilting. Attached to a standard (sic) = 12.7 mm mirror, the system has a resonance-free mechanical bandwidth up to 51 kHz, with displacements up to 2 mu m at 8 kHz. The maximum static steering error is 5.5 mu rad/mu m displaced, and the dynamic steering error is lower than 0.6 mu rad mu m(-1). This simple design should be useful for a large set of optical applications where tilt-free displacements are required, and we demonstrate its application in an ensemble of cold atoms trapped in periodically driven optical lattices. Published by AIP Publishing.