  Gravitational scattering in the ADD-model is studied and it is argued that no
cut-off is needed for the exchange of virtual Kaluza--Klein modes. By
introduction of a small coordinate in the extra dimensions a unique form of the
Kaluza--Klein-summed propagator is found for an odd number of extra dimensions.
The matrix element corresponding to this propagator can also (as opposed to the
cut-offed version) be Fourier transformed to position space, giving back the
extra-dimensional version of Newton's law. For an even number of extra
dimensions the propagator is found by requiring that Newton's law should be
recovered.
