  Clifford indices for semistable vector bundles on a smooth projective curve
of genus at least 4 were defined in previous papers of the authors. In the
present paper, we establish lower bounds for the Clifford indices for rank 3
bundles. As a consequence we show that, on smooth plane curves of degree at
least 10, there exist non-generated bundles of rank 3 computing one of the
Clifford indices.
