The accuracy of ocean tide predictions is relatively low in the Southern Ocean, and this has negative consequences for measuring the mass balance of Antarctic ice shelves and the circulation of the Southern Ocean with altimetry and Grace data. New empirical estimates of ocean and ice shelf tides based on CryoSat-2 data are now being used to provide better observational constraints on dynamical ocean tide models. The main sources of uncertainty in the dynamical models are the representation of dissipation, both under-ice-shelf and bottom-boundary-layer drag, uncertain water column thickness, especially under ice shelves, and the coupling of the subinertial diurnal tides to the non-tidal circulation. Here, Egbert and Erofeeva's OTIS variational assimilation system is extended to incorporate water column thickness as a control variable, and used to assess the adjoint sensitivity of tidal elevation to the model uncertainties. It is found that new parameterizations of dissipation and diurnal tidal/non-tidal coupling lead to slightly better agreement with CryoSat-2 data, but more significant improvement is obtained by assimilating the CryoSat-2 data to adjust the water column thickness. The presentation will discuss the accuracy of the new tidal elevations, as well as summarize efforts to validate the adjusted water column thickness by comparing the results for different tidal frequencies.