  Two branches of integrable open quantum-group invariant $D_{n+1}^{(2)}$
quantum spin chains are known. For one branch (epsilon=0), a complete Bethe
ansatz solution has been proposed. However, the other branch (epsilon=1) has so
far resisted solution. In an effort to address this problem, we consider here
the simplest case n=1. We propose a Bethe ansatz solution, which however is not
complete, as it describes only the transfer-matrix eigenvalues with odd
degeneracy. We also consider a proposal for the missing eigenvalues.
