The diffusive layering (DL) form of double-diffusive convection cools the Atlantic Water (AW) as it circulates around the Arctic Ocean. Large DL steps, with heights of homogeneous layers often greater than 10 m, have been found above the AW core in the Eurasian Basin (EB) of the eastern Arctic. Within these DL staircases, heat and salt fluxes are determined by the mechanisms for vertical transport through the high-gradient regions (HGRs) between the homogeneous layers. These HGRs can be thick (up to 5 m and more) and are frequently complex, being composed of multiple small steps or continuous stratification. Microstructure data collected in the EB in 2007 and 2008 are used to estimate heat fluxes through large steps in three ways: using measured dissipation rate in the large homogeneous layers; utilizing empirical flux laws based on the density ratio and temperature step across HGRs after scaling to account for presence of multiple small DL interfaces within each HGR; and averaging estimates of heat fluxes computed separately for individual small interfaces (as laminar conductive fluxes), small convective layers (via dissipation rates within small DL layers), and turbulent patches (using dissipation rate and buoyancy) within each HGR. Diapycnal heat fluxes through HGRs evaluated by each method agree with each other, and range from ~2 W m^-2 to ~8 W m^-2, with an average flux of ~3-4 W m^-2. These large fluxes confirm a critical role for the DL instability in cooling and thickening the AW layer as it circulates around the eastern Arctic Ocean.