Output from an eddy-resolving model of the North Atlantic Ocean is used to estimate values for the thickness diffusivity κ appropriate to the Gent and McWilliams parameterization. The effect of different choices of rotational eddy fluxes on the estimated κ is discussed. Using the raw fluxes (no rotational flux removed), large negative values (exceeding −5000 m2 s−1) of κ are diagnosed locally, particularly in the Gulf Stream region and in the equatorial Atlantic. Removing a rotational flux based either on the suggestion of Marshall and Shutts or the more general theory of Medvedev and Greatbatch leads to a reduction of the negative values, but they are still present. The regions where κ 〈 0 correspond to regions where eddies are acting to increase, rather than decrease (as in baroclinic instability) the mean available potential energy. In the subtropical gyre, κ ranges between 500 and 2000 m2 s−1, rapidly decreasing to zero below the thermocline in all cases. Rotational fluxes and κ are also estimated using an optimization technique. In this case, |κ| can be reduced or increased by construction, but the regions where κ 〈 0 are still present and the optimized rotational fluxes also remain similar to a priori values given by the theoretical considerations. A previously neglected component (ν) of the bolus velocity is associated with the horizontal flux of buoyancy along, rather than across, the mean buoyancy contours. The ν component of the bolus velocity is interpreted as a streamfunction for eddy-induced advection, rather than diffusion, of mean isopycnal layer thickness, showing up when the lateral eddy fluxes cannot be described by isotropic diffusion only. All estimates show a similar large-scale pattern for ν, implying westward advection of isopycnal thickness over much of the subtropical gyre. Comparing ν with a mean streamfunction shows that it is about 10% of the mean in midlatitudes and even larger than the mean in the Tropics.