  There is an approach due to Bazhanov and Reshetikhin for solving integrable
RSOS models which consists of solving the functional relations which result
from the truncation of the fusion hierarchy. We demonstrate that this is also
an effective means of solving integrable vertex models. Indeed, we use this
method to recover the known Bethe Ansatz solutions of both the closed and open
XXZ quantum spin chains with U(1) symmetry. Moreover, since this method does
not rely on the existence of a pseudovacuum state, we also use this method to
solve a special case of the open XXZ chain with nondiagonal boundary terms.
