The impact of coupling the atmosphere to the surface energy balance is examined for the stable boundary layer, as an extension of the first GABLS (GEWEX Atmospheric Boundary-Layer Study) one-dimensional model intercomparison. This coupling is of major importance for the stable boundary-layer structure and its development because coupling enables a realistic physical description of the interdependence of the surface temperature and the surface sensible heat flux. In the present case, the incorporation of a surface energy budget results in stronger cooling (surface decoupling), and a more stable and less deep boundary layer. The proper representation of this is a problematic feature in large-scale numerical weather prediction and climate models. To account for the upward heat flux from the ice surface beneath, we solve the diffusion equation for heat in the underlying ice as a first alternative. In that case, we find a clear impact of the vertical resolution in the underlying ice on boundary-layer development: coarse vertical resolution in the ice results in stronger surface cooling than for fine resolution. Therefore, because of this impact on stable boundary-layer development, the discretization in the underlying medium needs special attention in numerical modelling studies of the nighttime boundary layer. As a second alternative, a bulk conductance layer with stagnant air near the surface is added. The stable boundary-layer development appears to depend heavily on the bulk conductance of the stagnant air layer. This result re-emphasizes the fact that the interaction with the surface needs special attention in stable boundary-layer studies. Furthermore, we perform sensitivity studies to atmospheric resolution, the length-scale formulation and the impact of radiation divergence on stable boundary-layer structure for weak windy conditions.