Diagnostic models of the tropical cyclone boundary layer have important practical uses, including engineering design and climatological risk-assessment studies and as components of tropical cyclone potential-intensity models. A widely used class of such models has been slab models, in which the governing equations are depth-averaged. Here, a slab model is compared with one that fully resolves height, and it is shown that the vertical averaging leads to substantial differences in the simulations. The slab model produces excessively strong inflow and too great a departure of the boundary-layer mean winds from gradient balance. In moving storms, the slab models produce much too strong a motion-induced asymmetry, and can support an asymmetric analogue of the quasi-inertial oscillation previously noted in axisymmetric slab models. Given the considerable impact of the vertical averaging in slab models on the simulated flow in the tropical cyclone boundary layer, it is difficult to recommend their further use for applications where quantitative accuracy is important. Other applications will require care to ensure that the results are not unduly affected by the depth averaging. Part II of this article presents a detailed analysis of the reasons for the differences between depth-averaged and height-resolving simulations of the tropical cyclone boundary layer. © 2010 Published by John Wiley & Sons, Ltd.