A one-dimensional model of the ocean near-surface currents is presented. It includes the enhanced near-surface mixing due to the waves, the wave-induced Stokes drift, the Stokes-Coriolis (SC) effect, and the stratification. Near-surface current shears from this model are compared with the shears of the quasi-Eulerian currents measured using a wave-following platform during the Shelf Mixed Layer Experiment (SMILE). It is shown that the downwind current shears observed during SMILE are well modeled. However, the observed crosswind shears are in poor agreement with the model. The Stokes-Coriolis (SC) term could qualitatively explain this misfit, but it is one order of magnitude too weak. The Ekman-Stokes spiral of the model is compared with the spiral observed during the long time series of measurements Long Term Upper Ocean Study 3. The effects of stratification are taken into account. The mean velocity profiles of the model closely agree with observations. However, there is no evidence of the SC effect on the shape of the observed current profile. The observed profile is found to be a consequence of the current rectification due to the time-varying stratification. The SC effect calculated from a numerical wave hindcast is weak but should have been observed. In fact, it is estimated that the wave-induced bias in the current measurements is larger than the SC effect. Finally, it is shown that the variation of surface drift with wave age, which was estimated to be small in unstratified conditions, is important in the presence of shallow mixed layers.