While the equation of state for copper has been fairly well studied, wave speeds at low stress are not as well known. Systematic errors may be present in the lowest stress data presented in the Marsh  compendium due to the use of the flash gap method to collect the data. Additionally, little data has been gathered on the wave speeds in single-crystal copper, which may vary from polycrystalline due to the different longitudinal and shear sound speeds. Hugoniot information at low pressures is useful in constraining and improving predictive hydrodynamic codes. Knowledge of single-crystal behavior provides input for mesoscale computer models that use tens-of-micron-sized grains of single crystals to build a model of polycrystalline systems. We undertook experiments to measure wave speeds in polycrystalline and single-crystal copper at low pressures using a novel technique to limit error, and to determine if single-crystal shock velocities are systematically different than polycrystalline shock velocities at the same stress. The best previous research on this topic is from Chau et al.  at relatively high shock stress; they reported no observed difference between orientations. It is of interest to do careful measurements at low stress, and that is the principal goal of this work.