A nonlinear optimal control law based on a quartic cost function is developed, and applied to a quarter-car vehicle model. For small disturbances, the performance is similar to the "soft" linear suspension, but for large disturbances, the suspension travel and wheel hop are reduced at the expense of larger body acceleration. The nonlinear suspension controller qualitatively emulates an LQ controller gain scheduled by RMS input levels, and provides a safer ride than the linear controller.