While it is known that softness discrimination relies on both kinesthetic and cutaneous information, relatively little work has been done on the realization of haptic devices replicating the two cues in an integrated and effective way. In this paper, we first discuss the ambiguities that arise in unimodal touch, and provide a simple intuitive explanation in terms of basic contact mechanics. With this as a motivation, we discuss the implementation and control of an integrated device, where a conventional kinesthetic haptic display is combined with a cutaneous softness display. We investigate the effectiveness of the integrated display via a number of psychophysical tests and compare the subjective perception of softness with that obtained by direct touch on physical objects. Results show that the subjects interacting with the integrated haptic display are able to discriminate softness better than with either a purely kinesthetic or a purely cutaneous display.