The force needed to pull a cylindrical stud from a soft elastomeric film depends on their elastic and geometric properties. For a rigid stud and a thick elastomeric film, the pull-off stress (sigma) depends on the elastic modulus (E) of the film and the radius (a) of the stud as sigma similar to (E/a)(1/2) (soft adhesion). However, when the film is very thin, the pull-off stress is significantly higher than the case with thick films, and its value depends on the elastic modulus and the thickness (h) of the film as sigma similar to (E/h)(1/2) (hard adhesion). Here, we study the pull-off behavior of a soft cylindrical stud, one flat end of which is coated with a high modulus thin baseplate. As the flexural rigidity of this baseplate is varied, we observe the transition between the two types of adhesion. We present a simple physical interpretation of the problem, which could be of value in understanding various biofouling and adhesive situations.