  For a hyperbolic 3-manifold M with a torus boundary component, all but
finitely many Dehn fillings on the torus component yield hyperbolic
3-manifolds. In this paper, we will focus on the situation where M has two
exceptional Dehn fillings, both of which yield toroidal manifolds. For such
situation, Gordon gave an upper bound for the distance between two slopes of
Dehn fillings. In particular, if M is large, then the distance is at most 5. We
show that this upper bound can be improved by 1 for a broad class of large
manifolds.
