  If a graph is in bridge position in a 3-manifold so that the graph complement
is irreducible and boundary irreducible, we generalize a result of Bachman and
Schleimer to prove that the complexity of a surface properly embedded in the
complement of the graph bounds the graph distance of the bridge surface. We use
this result to construct, for any natural number $n$, a hyperbolic manifold
containing a surface of topological index $n$.
