Active haptic discrimination of mathematically well-defined surfaces was investigated. The quadric surfaces were defined in terms of 'shape index'--a quantity describing shape--and 'curvedness'--a quantity describing overall curvature. In these experiments shape index was varied and curvedness kept constant. The influence of laterality (unilateral versus bilateral discrimination) was tested in separate sessions. No influence of shape on the discrimination of solid objects was found. From the results an estimate can be made of the just-noticeable difference in terms of shape-index units. There was a significant effect of laterality on discrimination: performance with unilateral (successive) examination (both with left and with right hand) was better than with bilateral (simultaneous) examination.