  We calculate the mass shifts of heavy-light scalar mesons due to hadronic
loops under the assumption that these vanish for the groundstate heavy-light
mesons. The results show that the masses calculated in quark models can be
reduced significantly. We stress that the mass alone is not a signal for a
molecular interpretation. Both the resulting mass and the width suggest the
observed $D_0^*$ state could be a dressed $c\bar q$ state. We give further
predictions for the bottom scalar mesons which can be used to test the dressing
mechanism.
