Understanding the complementary roles of surface energy and roughness on natural nonwetting surfaces has led to the development of a number of biomimetic superhydrophobic surfaces, which exhibit apparent contact angles with water greater than 150 degrees and low contact angle hysteresis. However, superoleophobic surfaces-those that display contact angles greater than 150 degrees with organic liquids having appreciably lower surface tensions than that of water-are extremely rare. Calculations suggest that creating such a surface would require a surface energy lower than that of any known material. We show how a third factor, re-entrant surface curvature, in conjunction with chemical composition and roughened texture, can be used to design surfaces that display extreme resistance to wetting from a number of liquids with low surface tension, including alkanes such as decane and octane.