  Given a closed hyperbolic 3-manifold M of volume V, and a link L in M such
that the complement M \ L is hyperbolic, we establish a bound for the systole
length of M \ L in terms of V. This extends a result of Adams and Reid, who
showed that in the case that M is not hyperbolic, there is a universal bound of
7.35534... . As part of the proof, we establish a bound for the systole length
of a non-compact finite volume hyperbolic manifold which grows asymptotically
like (4/3)log(V).
