  We consider the open XXZ quantum spin chain with nondiagonal boundary terms.
For bulk anisotropy value \eta = i \pi/(p+1), p= 1, 2, ..., we propose an exact
(p+1)-order functional relation for the transfer matrix, which implies
Bethe-Ansatz-like equations for the corresponding eigenvalues. The key
observation is that the fused spin-(p+1)/2 transfer matrix can be expressed in
terms of a lower-spin transfer matrix, resulting in the truncation of the
fusion hierarchy.
