Abstract. The use of a boundary-layer parameterization of buttressing and ice flux across grounding lines in a two-dimensional ice-sheet model is improved by allowing general orientations of the grounding line. This and another modification to the model's grounding-line parameterization are assessed in two settings: a narrow fjord-like domain (MISMIP+), and in future simulations of West Antarctic ice retreat under RCP8.5-based climates. The new modifications are found to have significant effects on the fjord results, which are now within the envelopes of other models in the MISMIP+ intercomparison. In contrast, the modifications have little effect on West Antarctic retreat, presumably because dynamics in the wider major Antarctic basins are adequately represented by the model's previous simpler one-dimensional formulation. As future grounding lines retreat across very deep bedrock topography in the West Antarctic simulations, buttressing is weak and deviatoric stress measures exceed the ice yield stress, implying that structural failure at these grounding lines would occur. We suggest that these grounding-line quantities should be examined in similar projections by other ice models, to better assess the potential for future structural failure.