Super-hydrophobic surfaces may arise due to an interplay between the intrinsic, relatively high, contact angle of the more or less hydrophobic solid surface employed and the geometric features of the solid surface. In the present work, this relationship was investigated for a range of different surface geometries, making use of surface free energy minimization. As a rule, the free energy minima (and maxima) occur when the Laplace and Young conditions are simultaneously fulfilled. Special effort has been devoted to investigating the free energy barriers present between the Cassie-Baxter (heterogeneous wetting) and Wenzel (homogeneous wetting) modes. The predictions made on the basis of the model calculations compare favorably with experimental results presented in the literature.