  We investigate gravitational perturbations in a compact six-dimensional
self-tuning brane model. We specifically look for analytic solutions to the
perturbed Einstein equations that correspond in four-dimensions to massless or
approximately massless scalars coupled to matter on the brane. The presence of
such modes with gravitational couplings would be phenomenologically
unacceptable. The most general solution for all such modes is obtained, but it
is found that they are all eliminated by the boundary conditions. Our main
result is that to linear order in perturbation theory this model does not
contain any light scalars. We speculate that this model does not self-tune.
