Computational results from Navier-Stokes equations are presented for the Stokes-wave/flat-plate boundary-layer and wake for small wave steepness(Ak=0.01), including exact and approximate treatments of the viscous free-surface boundary conditions. The macro-scale flow indicate that the variations of the external-flow pressure gradients cause acceleration or deceleration of the streamwise velocity component and alternating direction of the cross flow. Remarkably, the wake displays a greater response, i.e., a bias with regard to favorable as compared to adverse pressure gradients. The micro-scale flow indicates that the free-surface boundary conditions have a profound influence over the boundary layer and near/intermediate wake. Order-of-magnitude estimates are conformed to the computational results. And appreciable errors are introduced through approximations to the free-surface boundary conditions.