[1] We perform a series of 3-D Direct Numerical Simulations (DNS) to assess the vertical heat transport through thermohaline staircases in the Arctic Ocean. The diagnostics of DNS, performed for the first time in the realistic parameter range, result in vertical fluxes exceeding those of extant "four-thirds flux laws" by as much as a factor of 2 and suggest that the 4/3 exponent may require downward revision. Through a series of equivalent 2-D DNS, we show that they are consistent with their more resource-intensive 3-D counterparts for sufficiently large density ratio (R r ) but underestimate heat transport for low R r . Finally, we examine the role of boundary conditions in controlling the vertical heat transport. Rigid boundaries-a necessary ingredient in laboratoryderived flux-laws-are shown to reduce the estimates of heat fluxes relative to the corresponding periodic boundary conditions.