We investigate the plausibility of salinity-driven free (thermohaline) convection in sedimentary rocks of the south Texas part of the Gulf of Mexico basin using salinity data, Rayleigh number calculations, and numerical models. Previous studies speculated that free convection could account for high fluxes evidently required for diagenesis in the basin, but low-permeability shales are calculated to be a barrier to free convection. In the study area, salinity inversions occur either above or within the transition zone from hydropressures to overpressures. The positioning of brines over less saline fluids provides a significant buoyancy force. Rayleigh number calculations and numerical simulations suggest that homogeneous shaly systems are unstable near the high end of the expected ranges of shale permeability (10-15-10-16 m2). Numerical simulations show that the influx of brine into the permeable layers and permeability heterogeneity in the shales are both conducive to free convection. Simulations indicate that salinity-driven free convection can occur at lower permeabilities (10-16-10-18 m2) that may approximate the permeabilities of shales in the zone of extreme overpressures over geologic time. Simple Rayleigh numbers are inadequate to predict the occurrence of free convection in heterogeneous systems. Salinity-driven free convection at depths in some large sedimentary basins, such as the Gulf of Mexico, may be more common than expected.