  We give new bounds for the distance between two exceptional filling slopes
for a 1-cusped hyperbolic 3-manifold in several different situations. The
distance between a reducible slope and a slope that produces a manifold with
finite fundamental group is at most 2. The distance between a reducible slope
and one that produces a very small manifold is also at most 2. The distance
between a reducible slope and one which produces a manifold with a pi_1
injective torus is at most 4. The methods used involve both characteristic
submanifold theory and the theory of the PSL(2,C) character variety.
