  We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary
terms. By exploiting certain functional relations at roots of unity, we propose
the Bethe ansatz solution for the transfer matrix eigenvalues for cases where
atmost two of the boundary parameters are set to be arbitrary and the bulk
anisotropy parameter has values \eta = i \pi/3, i \pi/5,... We present
numerical evidence to demonstrate completeness of the Bethe ansatz solutions
derived for s = 1/2 and s = 1.
