Accurate integral properties of plane periodic deep-water waves of amplitudes up to the steepest are tabulated by Longuet-Higgins (1975). These are used to define an averaged Lagrangian which, following Whitham, is used to describe the properties of slowly varying wave trains. Two examples of waves on large-scale currents are examined in detail. One flow is that of a shearing current, V (x) j, which causes waves to be refracted. The other flow, U (x) i, varies in the direction of wave propagation and causes waves to either steepen or become more gentle. Some surprising features are found.