  Recent renormalization group studies of impurities in spin-1/2 chains appear
to be inconsistent with Bethe ansatz results for a special integrable model. We
study this system in more detail around the integrable point in parameter space
and argue that this integrable impurity model corresponds to a non-generic
multi-critical point. Using previous results on impurities in half-integer spin
chains, a consistent renormalization group flow and phase diagram is proposed.
