  We study the reflection amplitudes of affine Toda field theories with
boundary, following the ideas developed by Fring and Koberle and focusing our
attention on the $E_{n}$ series elements, because of their interesting
structure of higher order poles. We also investigate the corresponding minimal
reflection matrices, finding, with respect to the bulk case, a more complicated
relation between the spectra of bound states associated to the minimal and to
the ''dressed'' amplitudes.
