New rates of decay are presented for temporally-attenuated gravity waves in deep water, allowance being made for the energy dissipated in the Stokes interfacial boundary layer in the air. This decay-rate, involving air drag, may then be used to deduce a new “free-surface” boundary condition for the problem of the mass transport velocity due to progressive waves; for shallow-water waves, two specific velocity profiles are calculated, and indicate large differences in comparison with the corresponding profiles of Longuet-Higgins (1953) for a vacuum-water interface.