Precision measurements indicate that the stability capping of the neutral planetary boundary layer (PBL) that leads to a reduced PBL height is caused by the very stable upper part of the PBL, rather than by an overlying inversion. Radiative processes related to liquid water in boundary-layer clouds seem to play the key role for the formation of the stable upper PBL. The famous Leipzig Profile – generally considered as an example of a neutral PBL – has been included in Hess's analysis because its PBL height is considerably lower than the ca. 3000 m to be expected by numerical models in truly neutral conditions. An analysis of the original observations reveals that the Leipzig PBL was stable and that it can be consistently treated as a ‘normal’ stable PBL with a height of ca. 700 m. A further finding is that the super-geostrophic PBL wind speed maxima predicted by almost all models are not observed in near-steady-state conditions. For the ‘ranking’ of analytical models versus numerical models, the comparisons with measurements show that the analytical models perform comparably well and even partially better than the numerical models.