We theoretically model the combined dry and wet adhesion between a rigid sphere and an elastic substrate, where the dry contact area is surrounded by a liquid meniscus. The influence of the liquid on the interfacial adhesion is twofold: inducing the Laplace pressure around the dry contact area and altering the adhesion energy between solid surfaces. The behavior of such combined dry and wet adhesion shows a smooth transition between the JKR and DMT models for hydrophilic solids, governed by the prescribed liquid volume or environmental humidity. The JKR-DMT transition vanishes when the solids become hydrophobic. An inverse scaling law of adhesive strength indicates that size reduction helps to enhance the adhesive strength until a theoretical limit is reached. This study also demonstrates the jumping-on and jumping-off hysteresis between the combined dry-wet adhesion and pure liquid bridge in a complete separation and approach cycle. (C) 2016 Elsevier Inc. All rights reserved.