A number of problems related to mesoscale numerical prediction of low stratus in the Alpine region are formulated, and addressed in a series of experiments for two wintertime cases. These problems include modelling aspects and issues of data assimilation which are relevant particularly in relation to the observation nudging technique. A focus is on the influence of orography. A comparison of operational optimum interpolation, and nudging of routine rawinsonde and surface-level data reveals that nudging often yields better analyses and forecasts of low stratus, and notably of the sharp vertical temperature and humidity gradients. However, the humidity advection scheme of the model and, near steep terrain, particularly the horizontal diffusion along the model's σ-levels are identified to contribute to spurious vertical smoothing which can result in erroneous cloud dissipation. On occasions, forecasts succeeding a nudging period are more sensitive to this process due to the sharper initial vertical gradients. Specific problems of representiveness arise when low-level rawinsonde information is spread laterally along the sloping σ-levels from low to high terrain. A new concept for σ-layer models is introduced by speading the observational information along isentropic surfaces, and this tends to improve the low stratus prediction over steep and even moderate orography. A partly successful attempt to take advantage of the steep Alpine orography is made by applying this concept to surface-level humidity data from a high-resolution network of Alpine surface stations which are distributed relatively uniformly in the vertical.