We present a theoretical study of the conformations of a polymer brush (made of linear macromolecules chemically anchored to a flat, solid interface) when it is exposed to a molten, compatible polymer. At large brush grafting densities a and melt molecular weights P, the melt only penetrates the brush over a distance lambda that is small, compared to the brush thickness. For P > N(2/3)sigma(-2/3), the penetration length lambda approximate to a sigma(-1/3)N(1/3) (Leibler et al. Proceedings of the GUMS Conference, Osaka, Japan, June, 1993) is associated with partial wetting. Far P < N(2/3)sigma(-2/3), although wetting is complete (as was predicted by Leibler et al), we find that penetration is still partial : lambda = a sigma(-1)NP(-1). There should be implications in interfacial rheology and in wetting dynamics.