Exceptional surgeries on knots with exceptional classes

We survey the aspects of classical combinatorial sutured manifold theory and show how they can be adapted to study exceptional Dehn fillings and 2-handle additions. As a consequence, we show that if a hyperbolic knot beta in a compact, orientable, hyperbolic 3-manifold, M has the property that winding number and wrapping number are not equal with respect to a non-trivial class in H2( M, partial derivative M), and then, with only a few possible exceptions, every 3-manifold M' obtained by Dehn surgery on beta with surgery distance Delta >= 2 will be hyperbolic.