Mesoscale eddies modify the rate at which a water mass transfers from the surface mixed layer of the ocean into the interior thermocline, in particular in regions of intense baroclinic instability such as the Antarctic Circumpolar Current, open-ocean convective chimneys, and ocean fronts. Here, the time-mean subduction of a water mass, evaluated following the meandering surface density outcrops, is found to incorporate a rectified contribution from eddies, arising from correlations between the area over which the water mass is outcropped at the sea surface and the local subduction rate. Alternatively, this eddy subduction can be interpreted in terms of an eddy-driven secondary circulation associated with baroclinic instability. The net subduction rate, incorporating both Eulerian-mean and eddy contributions, can be further related to buoyancy forcing of the surface mixed layer using a formula by Walin (1982). Solutions from an idealized two-dimensional ocean model are presented to illustrate the eddy contribution to subduction rates in the Southern Ocean and in an open-ocean convective chimney. In the Southern Ocean, the net subduction rate is the residual of the Eulerian-mean and eddy contributions, which cancel at leading order; given plausible patterns of surface buoyancy forcing, one can obtain subduction of Antarctic Intermediate Water and Antarctic Bottom Water, with entrainment of North Atlantic Deep Water in between. In a convective chimney, in contrast, the Eulerian-mean subduction rate is vanishingly small and the subduction is contributed entirely by mesoscale eddies.