Ice-flow modelling continues to be challenging due to the need to balance computational efficiency with physical complexity, a choice that directly affects the accuracy of sea-level projections. Several recent studies have successfully introduced a numerical stabilisation scheme to Stokes models that reduces the stiffness of the system of equations by predicting the ice geometry at the next time step, allowing for a larger time-step size without loss of accuracy [1,2,3]. However, the high physical complexity of Stokes models nonetheless renders them infeasible in large-scale simulations, in part due to memory restrictions. To address these limitations, we introduce the Thickness Stabilisation Scheme (TSS) for the Shallow Shelf Approximation (SSA). This numerical stabilisation scheme is constructed by modifying the momentum equations with terms that predict the ice thickness at the next time step, thereby also reducing the stiffness of the problem. In order to investigate the accuracy and efficiency of TSS, we perform numerical experiments of idealised ice shelves, varying the time-step size. The results show that the inclusion of the TSS allows for a significantly larger time-step size. The improved efficiency of SSA simulations through the inclusion of the TSS enables the reallocation of computational resources towards increased spatial resolution and greater physical complexity. [1] G. Durand, O. Gagliardini, B. de Fleurian, T. Zwinger, E. Le Meur., Marine ice sheet dynamics: Hysteresis and neutral equilibrium, Journal of Geophysical Research, 114(F3):F03009, 2009. [2] A. Löfgren, J. Ahlkrona, C. Helanow, Increasing stable time-step sizes of the free-surface problem arising in ice-sheet simulations, Journal of Com- putational Physics: X, 16:100114, 2022. [3] A.C.J. Henry, T. Zwinger, J. Ahlkrona, Grounding-line dynamics in a stokes ice-flow model: Improved numerical stability allows larger time steps, EGUsphere, 2025.