We have systematic experimental observations that just below the wetting transition of a polystyrene (PS) melt onto a substrate covered by a poly-4-vinylpyridine-PS (PVP/PS) di-block copolymer there can be a macroscopic droplet and two coexisting layer thicknesses of PS, In addition to the usual macroscopic droplet and a microscopically thin film at the substrate (typical for partial wetting), a second mesoscopically thick film is selected. This film is a polymer brush of order 10 nm thick swollen with free PS chains. The presence of this extra mesoscopically thick film proves that the wetting behavior near the wetting transition is richer than predicted by the classical wetting theory. The disjoining potential profile must be a function with two local minima near the surface instead of just one. We have seen the selection of this mesoscopic film thickness in the dewetting behavior of an unstable spin-coated film of PS on the brushed interface. The self-consistent field theory applied to this problem shows that a mesoscopically thick film may be trapped in a brush: there is a prewetting transition in combination with partial wetting.