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We show that if M is a simple 3-manifold bounded by two tori such that M(r1) is reducible and M(r2) is toroidal, then Δ(r1, r2) ≤ 2, answering a question raised by Gordon. To do this, we first prove that there exists only one simple 3-manifold having two Dehn fillings of distance 3 apart one of which yields a reducible manifold and the other yields a 3-manifold containing a Klein bottle.

Reducing and toroidal Dehn fillings on $3$-manifolds bounded by two tori