The paper discusses recent developments aimed at improving the efficiency by which converged first and second-order results may be obtained. A higher-order element discretization of a novel integral equation is described. It is shown that this is capable of providing highly accurate first-order results based on a relatively small number of elements. Results are also given for the nonlinear diffraction problem, including comparisons with an analytical solution for a vertical cylinder. Practical use of these developments is illustrated by results for the second-order free surface profile in the vicinity of a tension leg platform.