The effects of tunnelling from the p states of the scanning microscope tip are considered. In the case of the graphite surface, it is shown that an appreciable tunnel current flows to the p_x and p_y components of the tip wavefunction and that this tunnel current significantly reduces the amplitude of the corrugations that should be measured on this surface. The results also show that the giant corrugations observed in scanning tunnelling microscope images of graphite cannot be explained by a tunnelling model.