The problem of diffusive shock acceleration of fast charged particles is reexamined with emphasis on the rate of energy gain, and the maximum energy which can be attained in a given circumstance. The direction of the average magnetic field at the shock is shown to have a large effect. If the perpendicular diffusion coefficient is much smaller than the parallel coefficient, particles can gain much more energy if the shock is quasi-perpendicular than if it is quasi-parallel. The maximum energy attainable can be substantially higher (by a factor of 100 or more) than previous discussions would predict, in cases where the shock is quasi-perpendicular. The energy gain increases as kappa-perpendicular decreases. The principal limitation comes from the requirement that diffusion be a valid approximation to the particle motion, and that the particle be able to diffuse fast enough to encounter the shock many times.