The advent of high precision gravity missions presents the opportunity to accurately measure variations in the distribution of mass in the ocean. Such a data source will prove valuable in state estimation and constraining general circulation models (GCMs) ingeneral. However, conventional GCMs make the Boussinesq approximations, a consequence of which is that mass is notconserved. By use of the height-pressure coordinate isomorphism implemented in the MITgcm, the impact of non-Boussinesq effects can be evaluated. Although implementing a non-Boussinesq model in pressure coordinates is relatively straight-forward, making a direct comparison between height and pressure coordinate (i.e., Boussinesq and non-Boussinesq) models is not simple. But a careful comparison of the height coordinate and the pressure coordinate solutions ensures that only non-Boussinesq effects can be responsible for the observed differences. As a yard-stick, these differences are also compared to those between the Boussinesq hydrostatic and models in which the hydrostatic approximation has been relaxed, another approximation commonly made in GCMs. Model errors (differences) due to the Boussinesq and hydrostatic approximations are demonstrated to be of comparable magnitude. Differences induced by small changes in sub-grid scale parameterizations are at least as large. Therefore, non-Boussinesq and non-hydrostatic effects are most likely negligible with respect to other model uncertainties. However, because there is no additional cost incurred in using apressure coordinate model, it is argued that non-Boussinesq modeling is preferable simply for tidiness. It is also concluded that even coarse resolution GCMs can be sensitive to small perturbations in the dynamical equations.