Ardhuin et al. (2008) gave a second-order approximation in the wave slope of the exact Generalized Lagrangian Mean (GLM) equations derived by Andrews and McIntyre (1978), and also performed a coordinate transformation, going from a from GLM to a ’GLMz’ set of equations. That latter step removed the wandering of the GLM mean sea level away from the Eulerian-mean sea level, making the GLMz flow non-divergent. That step contained some inaccuarate statements about the coordinate transformation, while the rest of the paper contained an error on the surface dynamic boundary condition for viscous stresses. I am thankful to Mathias Delpey and Hidenori Aiki for pointing out these errors, which are corrected below.