By a consistent application of the distorted-wave Born approximation, the Debye-Waller exponent for the scattering of He atoms from the Ag(111) surface is directly computed. When diffraction is negligible, as in this case, the decrease in specular intensity is simply obtained by summing the scattering due to all possible one-phonon processes. Using one-phonon computed intensities that agree with experiment along high-symmetry directions of the surface Brillouin zone, we find that the computed Debye-Waller exponent agrees with experiment and corresponds to an effective Debye temperature of 241 K. All corrections to the eikonal-type formula, 2W=4pz2〈uz2〉, are automatically included. In particular, the contribution of phonons with high parallel momentum is sharply cut off.