The JKR test, which consists of investigating the contact between an elastic lens and a rigid substrate, is a local and precise adhesion test. However, in the classical JKR mechanical analysis, the dimensions of the system must be large compared to the size of the contact area; we consider here a rigid substrate coated with a thin layer of a softer material. We show that this case cannot be analysed using the JKR theory. We propose a simple mechanical approach, modeling the layer as an elastic mattress, which accounts for the experimentally observed phenomena.