We consider the wet adhesion between two deformable fibers. We show that a strong adhesive force can be maintained by coupling the fibers deformation with capillarity. We further identify a regime where, contrary to capillary adhesion, the pull-off force remains constant throughout debonding. In this peeling regime, elasticity, which tends to minimize the deformation of the object, is balanced by capillarity which maximizes the liquid spreading. We show that the adhesive force and the existence region of this self-adjusted peeling regime depend on a single dimensionless parameter, and can thus be controlled by tuning the material properties.