The Boussinesq approximation is commonly made in ocean general circulation models (OGCMs). As a consequence, the model ocean is incompressible and conserves volume, but not mass. It has been argued that these consequence introduce errors at the noise level of coarse OGCMs, but that non-Boussinesq modeling is preferable simply for tidiness. Here, we use the height-pressure coordinate isomorphism implemented in the MITgcm to construct a non-Boussinesq OGCM and revisit the differences between Boussinesq and non-Boussinesq models at a resolution comparable to IPCC climate models. Subtleties such as the choice of a proper equation of state that includes the effect of pressure on heat capacity, but also the use of mass as a convenient alternative to pressure coordinates are discussed.