An idealized model for a convective basin is used to investigate the mechanisms of variability of the formation and export of dense water. In this model, which consists of two isopycnic layers, dense water formation is induced by surface buoyancy loss in the interior, which is at rest. Newly formed dense water is transmitted to the surrounding boundary current through parameterized eddy fluxes. Variability in the formation and export of dense water is due to changes in the two main drivers: variations in the surface buoyancy fluxes and variations in the large-scale wind via a barotropic boundary current. Numerical integrations of the nonlinear model, with parameters and forcings corresponding to the Labrador Sea, show that the rate of dense water formation in the interior of the basin is strongly affected by changes in the buoyancy forcing, but not significantly affected by seasonal to interannual changes in the wind-driven barotropic boundary current. The basin tends to integrate the buoyancy forcing variability with a memory time scale set by eddies, which is decadal for the Labrador Sea. Variability in dense water export, on the contrary, is strongly affected by changes in the wind-driven barotropic boundary current but hardly affected by changes in buoyancy forcing. Indeed changes in the transport of dense water at the basin outflow are dominated by those at the basin inflow, which, in this model, are directly related to fluctuations in the wind-driven barotropic boundary current. These results, which are consistent with analytical solutions of the linear model, suggest that fluctuations in the surface buoyancy fluxes in the interior Labrador Sea have little impact on the interannual variability of the dense water transport by the Deep Western Boundary Current at the outflow of the Labrador Sea, which is dominated by fluctuations in the wind-driven North Atlantic subpolar gyre, but influence the formation and export of recently ventilated waters.