Experiments were performed on a (100) copper single crystal to examine the influences that small displacement oscillations used in continuous stiffness measurement techniques have on hardness and elastic-modulus measurements in nanoindentation experiments. For the commonly used 2-nm oscillation, significant errors were observed in the measured properties, especially the hardness, at penetration depths as large as 100 nm. The errors originate from the large amount of dynamic unloading that occurs in materials like copper that have high contact stiffness resulting from their high modulus-to-hardness ratios. A simple model for the loading and unloading behavior of an elasticplastic material is presented that quantitatively describes the errors and can be used to partially correct for them. By correcting the data in accordance with model and performing measurements at smaller displacement oscillation amplitudes, the errors can be reduced. The observations have important implications for the interpretation of the indentation size effect.