  We apply results from both contact topology and exceptional surgery theory to
study when Legendrian surgery on a knot yields a reducible manifold. As an
application, we show that a reducible surgery on a non-cabled positive knot of
genus g must have slope 2g-1, leading to a proof of the cabling conjecture for
positive knots of genus 2. Our techniques also produce bounds on the maximum
Thurston-Bennequin numbers of cables.
