  We demonstrate that the generalization of the Coleman-Thun mechanism may be
applied to the situation, when considering scattering processes in
1+1-dimensions in the presence of reflecting boundaries. For affine Toda field
theories we find that the binding energies of the bound states are always half
the sum over a set of masses having the same colour with respect to the
bicolouration of the Dynkin diagram. For the case of $E_6$-affine Toda field
theory we compute explicitly the spectrum of all higher boundary bound states.
The complete set of states constitutes a closed bootstrap.
