  We discuss the impact of viscosity on nonlinear propagation of surface waves
at the interface of air and a fluid of large depth. After a survey of the
available approximations of the dispersion relation, we propose to modify the
hydrodynamic boundary conditions to model both short and long waves. From them,
we derive a nonlinear Schr\"odinger equation where both linear and nonlinear
parts are modified by dissipation and show that the former plays the main role
in both gravity and capillary-gravity waves while, in most situations, the
latter represents only small corrections. This provides a justification of the
conventional approaches to damped propagation found in the literature.
