Design of offshore structures requires knowledge of the appropriate current profile to be used in conjunction with the design wave. Accurate determination of the current profile will depend on reliable current models. Vertical transfer of momentum in storm-driven current models is commonly treated either by using eddy viscosity or by assuming 'slab-like' mixed layer flow. These two fundamentally different approaches predict different current speeds and profiles during severe storms. The existing data base is inadequate to determine which approach is better, but most existing data sets are subject to one or more of four limitations that can lead one improperly to interpret the data as supporting the existence of current velocity shear in otherwise uniform mixed layers. One-dimensional slab models are found to compare favorably with observed wind-driven currents at the Ocean Test Structure in the Gulf of Mexico (deployed in 20 m deep water). By using some reasonably simple assumptions, these slab models are able to replicate many of the significantly features of the wide range of different responses. The character of the response appears to depend on an interaction of stratification and topography. Barotropic responses are characteristic of typical coastal responses; current oriented longshore and are in phase with the wind. Baroclinic responses are dominantly inertial as might be expected in the deep sea, but with an additional near-bottom cross-shore counter flow. The structure of one observed barotropic response is compared to detail to predictions of both slab and eddy viscosity models and found consistent with a slab model and inconsistent with eddy viscosity models. Shear observed during this event was not significantly different from zero, but was significantly below estimated shear predictions of four eddy viscosity models given the peak 0.4 N/m2 wind stress.