This paper describes the development and evaluation of Undulating Covers (UnCovers), mobile interfaces that can change their surface texture to transmit information. The Pin Array UnCover incorporates sinusoidal ridges controlled by servomotors, which can change their amplitude and granularity. The Mylar UnCover is a more organic interface that exploits the buckling properties of Mylar, using muscle wires, to change the texture granularity. The results of two user studies show that very low frequency texture changes, using amplitude or granularity, can be distinguished with high levels of accuracy. Since small changes are perceptible, it is possible to incorporate such interfaces into mobile devices without drastically increasing their size or actuation requirements. Finally, ratings from participants indicate that UnCovers would be appropriate for attention-grabbing, or caring and supportive interpersonal messages.