For the perception of the hardness of compliant materials, several cues are available. In this paper, the relative roles of force/displacement and surface deformation cues are investigated. We have measured discrimination thresholds with silicone rubber stimuli of differing thickness and compliance. Also, the influence of the finger span is assessed. When compliance is expressed as the Young's modulus, the thresholds in the different conditions follow Weber's law with a Weber fraction of 15 percent. When the surface deformation cue was removed, thresholds more than trebled. Under the assumption of optimal cue combination, this suggests that a large fraction of the information comes from the surface deformation cue. Using a matching experiment, we found that differences in object thickness are correctly taken into account. When cues appear to contradict each other, the conflict is resolved by means of a compromise. © 2009 IEEE.