  In this paper we describe in detail the computation of the scattering
amplitudes of massive spin-2 Kaluza-Klein excitations in a gravitational theory
with a single compact extra dimension, whether flat or warped. These scattering
amplitudes are characterized by intricate cancellations between different
contributions: although individual contributions may grow as fast as ${\cal
O}(s^5)$, the full results grow only as ${\cal O}(s)$. We demonstrate that the
cancellations persist for all incoming and outgoing particle helicities and
examine how truncating the computation to only include a finite number of
intermediate states impacts the accuracy of the results. We also carefully
assess the range of validity of the low energy effective Kaluza-Klein theory.
In particular, for the warped case we demonstrate directly how an emergent low
energy scale controls the size of the scattering amplitude, as conjectured by
the AdS/CFT correspondence.
