In very gradually shoaling coastal water the energy of incident waves appears to be absorbed not by breaking at the upper surface, but predominantly by turbulent dissipation near the rippled sea bed. The question has been asked whether there can be then any wave set-up, that is any increase in the mean water level, at, or close to, the shoreline. The present investigation is in two parts. In the first, the bottom-boundary-layer is represented by a liquid of higher density and viscosity than the water above, and it is verified that the mean forward motion in the boundary-layer (the ”bottom-wind”) carries the viscous fluid up a plane beach as far as the breaker-line. There it is blocked and dissipated by the undertow and turbulence in the surf zone. The lower the amplitude of the incoming waves, the higher up the beach can the fluid in the boundary-layer penetrate. The second part of the paper is theoretical. The usual equations of wave energy and momentum in water of slowly varying depth are generalised so as to include the presence of a dissipative boundary layer at the bottom. It is then shown that the resulting equation for the mean surface slope can be integrated exactly, to give the mean surface depression (the “set-down”) in terms of the local wave amplitude and water depth, outside the surf zone. In the special case of a uniform beach slope s, a closed expression is obtained for the wave amplitude in terms of the local depth. It is shown that the waves can theoretically penetrate to the shoreline without breaking, for a sufficiently small value of s. In a practical example, corresponding to swell on the Atlantic coast of North America, it is found that s must be of order 10−3. The corresponding wave set-up is always negative and tends to zero at the beach.