Reducing Dehn filling and toroidal Dehn filling

It is shown that if M is a compact, connected, orientable hyperbolic 3-manifold whose boundary is a torus, and r1, r2 are two slopes on ∂M whose associated fillings are respectively a reducible manifold and one containing an essential torus, then the distance between these slopes is bounded above by 4. Under additional hypotheses this bound is improved. Consequently the cabling conjecture is shown to hold for genus 1 knots in the 3-sphere.