We report experimental results for the wetting states of a melt of polystyrene in contact with a brush, of polystyrene chains end-attached to a substrate. Wettability was assessed by monitoring the stability of an ultrathin film of the molten polymer; if the film remained stable and uniform for several days, it was considered to be a case of complete wetting, whereas spontaneous breakup (initiated by hole formation) was interpreted as partial wetting. The bare (oxidized silicon) substrate without the brush is partially wet. When the grafting density is varied, two wetting/dewetting transitions are found, depending on the length P of. the chains in the melt. At low grafting densities, a transition from partial to complete wetting is observed, which is driven by the swelling of the attached chains and their mixing with the melt. At a higher grafting density, there is a second wetting transition back to partial wetting which we ascribe to the poor mixing between stretched chains in the brush and free chains. The experimental results are compared with scaling relations and numerical self-consistent-field (SCF) calculations. For melts of chains that are short compared to the grafted chains, these calculations confirm the occurrence of two transitions. For much longer chains in the melt, the calculations predict that the contact angle remains finite, but its value remains very low over a certain window of grafting densities. Moreover, the calculations indicate that the zero contact angle can become metastable in this regime. This is consistent with the experimental finding that there is, also at high P, a window of grafting densities where no instabilities are found. Around the onset of instability, the films disproportionate into complicated patterns of dry surface, mesoscopic films, and droplets. These results suggest that the disjoining pressure has a double minimum structure, which is consistent with SCF calculations.