Active haptic discrimination of cylindrically curved hand-sized surfaces was investigated. Unilateral discrimination (that is, with one hand, either the left or the right one) was compared with bilateral discrimination. In this latter condition, the right hand had to touch the right surface, and the left hand the left one. The importance of which surface of the pair is placed to the right of the observer and which to the left (the so-called placement order) was also investigated. In comparison with existing studies, performance in the present experiments was better owing to the combined effects of a larger surface area and active instead of passive discrimination. The results show clearly that curvature discrimination does not follow a Weber law; performance is relatively better with the larger curvatures. For all subjects, unilateral discrimination was much better than bilateral discrimination. A partial cause of this difference is the influence of the placement order, which is very apparent in the results for the bilateral condition. These results cannot be fully explained but the findings suggest an influence of the object - observer relation on the perception of the object.