  Two definitions of the Clifford index for vector bundles on a smooth
projective curve $C$ of genus $g\ge4$ were introduced in a previous paper by
the authors. In another paper the authors obtained results on one of these
indices for bundles of rank 3. In this paper we extend these results in the
case where $C$ has classical Clifford index 3. In particular we prove Mercat's
conjecture for bundles of rank 3 for $g \leq 8$ and $g \geq 13$ when $C$ has
classical Clifford index 3. We obtain complete results in the case of genus 7.
