In the present study, we report a detailed investigation of the unusual size effect in single crystals. For the experiments we specified the hardness in single crystalline copper specimens with different orientations ( (001), (011) and (111)) using Oliver-Pharr method. Our results indicates that with decreasing load, after the value of the hardness reached its maximum, it starts to decrease for very small indentation depths (<150 nm). For the sake of accuracy of hardness determination we have developed two AFM-based methods to evaluate contact area between tip and indented material. The proposed exact measurement of the contact area, which includes the effect of pile-up and sink-in patterns, can partially explain the strange behaviour, however, the decrease of hardness at low loads is still observed. At higher loads range the specified hardness is practically constant.