Much attention has been recently given to the development of methods to produce super-hydrophobic surfaces. In most cases, these developments are done empirically, by trial and error. The objective of the present study is to find out which parameters should be given to the designer of a super-hydrophobic surface in order to enable a methodological approach, based on understanding the underlying mechanisms. To this end, the interrelationships between the main parameters that determine super-hydrophobicity (roll-off angle, apparent contact angle, contact angle hysteresis, and fraction of wetted area) are presented. It is demonstrated that all the studied parameters interrelate in such a way that it is enough to use the area fraction of the phi liquid-air interface within the roughness grooves as a design parameter. For a sufficiently high value of this parameter, the resulting super-hydrophobic surface is relatively insensitive to the specific form of the roughness, if the conditions for thermodynamic stability are fulfilled. (C) 2020 Published by Elsevier Inc.