We consider a free lattice field (a harmonic crystal) with a hard wall condition and a weak pinning to the wall. We prove that in a weak sense the pinning always dominates the entropic repulsion of the hard wall condition when the dimension is a least three. This contrasts with the situation in dimension one, where there is a so-called wetting transition, as has been observed by Michael Fisher. The existence of a wetting transition in the delicate two-dimensional case was recently proved by Caputo and Velenik. © 2000 American Institute of Physics.