  In this proceeding we present the nested Bethe ansatz for open spin chains of
XXX-type, with arbitrary representations (i.e. `spins') on each site of the
chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz
applies for a general $K^-(u)$, but a particular form of the $K^+(u)$ matrix.
We give the eigenvalues, Bethe equations and the form of the Bethe vectors for
the corresponding models. The Bethe vectors are expressed using a trace
formula.
