The possibility of making high-contact-angle, rough surfaces from low-contact-angle materials has recently been suggested and demonstrated. A thermodynamic analysis of this possibility in terms of feasibility and stability is presented. It turns out that only roughness topographies that conform to a feasibility condition which is developed in the present paper can support this phenomenon. Even under conditions that support the phenomenon, the high-contact-angle state may not be stable, and transition from the heterogeneous (Cassie-Baxter) wetting regime to the homogeneous (Wenzel) regime with a lower contact angle may occur. In addition, it is suggested to use the general terms hygrophilic and hygrophobic (based on the Greek prefix hygro- that means liquid) to describe low- and high-contact-angle surfaces, respectively.