Canuto and Dubovikov [Canuto, V.M., Dubovikov, M.S., 2006. Dynamical model of mesoscales in z-coordinates. Ocean Modelling, 11, 123-166; Canuto, V.M., Dubovikov, M.S., 2007. The effect of mesoscales on the tracer equation in z-coordinates OGCMs. Ocean Modelling 16, 17-27] claim that present oceanographic models ignore a leading-order diapycnal term in the mean buoyancy and tracer equations, while previously published work shows this is not the case. It is important for the density and tracer equations of ocean models to be diabatic only to the extent of imposed diapycnal mixing. Present ocean modelling practice does achieve this property but the equations and parameterizations of Canuto and Dubovikov do not. Canuto and Dubovikov also argue that the same "missing" term in the mean buoyancy equation leads to extra diapycnal advection across mean isopycnals that should be included in the diapycnal advection-diffusion balance in the deep ocean. We show that this is incorrect: the relevant mean diapycnal advection of the Munk-Wunsch advective-diffusive balance is caused by small-scale mixing processes and processes due to the non-linear nature of the equation of state, not by the four so-called "mesoscale-adiabatic" terms identified by Canuto and Dubovikov. Crown Copyright © 2006.