Laboratory experiments by earlier authors have shown that the near-surface velocity of an otherwise uniform current is reduced by following waves, but is increased by opposing waves. By a boundary-layer analysis with depth-dependent eddy viscosities, we show analytically that this is the consequence of second-order effects of wave–current interaction. Physical effects of waves on the current profile due to the moving free surface, wave attenuation and convective inertia are discussed. Comparisons with available experiments for smooth and rough seabeds are discussed. New predictions of the longitudinal variations along the current are made.