A Heegaard splitting is a decomposition of a 3-manifold into two handlebodies of equal genus. Its distance is defined to be the length of the shortest path in the curve complex of the splitting surface between the disk complexes of the two handlebodies. In 1987, A. Casson and C. Gordon showed that Dehn surgery on certain knots will produce strongly irreducible (distance at least 2) Heegaard splittings. I will discuss a new result that generalizes their work.