  We develop a unified formulation of the quantum inverse scattering method for
lattice vertex models associated to the non-exceptional $A^{(2)}_{2r}$,
$A^{(2)}_{2r-1}$, $B^{(1)}_r$, $C^{(1)}_r$, $D^{(1)}_{r+1}$ and $D^{(2)}_{r+1}$
Lie algebras. We recast the Yang-Baxter algebra in terms of novel commutation
relations between creation, annihilation and diagonal fields. The solution of
the $D^{(2)}_{r+1}$ model is based on an interesting sixteen-vertex model which
is solvable without recourse to a Bethe ansatz.
