Using a homemade setup, we investigated the adhesion between soft elastic substrates bearing surface microstructures (array of caps [resp., holes] of height [resp., depth] h) and a smooth surface of the same rubber. In the framework of the classical model developed by Johnson, Kendall, and Roberts, we show the following. (i) The existence of a critical height h c for the microstructures, resulting from a competition between the adhesion energy and the elastic deformation energy necessary to invade the pattern: for h h c , an air film remains intercalated in the microstructure, and the contact is limited to the top of the caps or between the holes. The transition between these two states can be induced by increasing the squeezing force. (ii) The adhesion energy, W, of intimate contacts (h < h c ) decreases as the height increases. Suspended contacts correspond to a low adhesion and a nearly Hertzian behavior.Using simple scaling arguments and a two-level energetic description (single microstructure and whole contact) we propose a semiquantitative description of these observations.