  We investigate the applicability of a random-matrix model to the description
of non-collective excitations in heavy-ion reactions around the Coulomb
barrier. To this end, we study fusion in the reaction $^{16}$O + $^{208}$Pb,
taking account of the known non-collective excitations in the $^{208}$Pb
nucleus. We show that the random-matrix model for the corresponding couplings
reproduces reasonably well the exact calculations, obtained using empirical
deformation parameters. This implies that the model may provide a powerful
method for systems in which the non-collective couplings are not so well known.
