We extend the construction of open descendants to the SU(2) WZW models with non-diagonal left-right pairing, namely E(7) and the D-odd series in the ADE classification of Cappelli, Itzykson and Zuber. The structure of the resulting models is determined to a large extent by the ''crosscap constraint'', while their Chan-Paton charge sectors may be embedded in a general fashion into those of the corresponding diagonal models.