Accurate one-way wave equations should simulate waveforms with a completeness that is intermediate between ray-based methods and full wave equation finite differences, for an intermediate computational effort. There is a hierarchy of one-way options, including exact coupled forward and backward operators which are mathematically equivalent to the omni-directional parent wave equation. We show numerical results obtained by using an approximate one-way equation with high-accuracy full wave equation finite-difference results, for both reflected and transmitted waves. The effects of lateral gradients in particular are discussed.