The equations governing buoyancy-driven convection in a rotating horizontal fluid layer, where the thermal expansion coefficient is a function of pressure (here, depth), have been derived. The results confirm the validity of the Boussinesq approximation. Furthermore, the adiabatic lapse rate for cold seawater is shown to be so small that it can usually be neglected in comparison to the in situ temperature gradient. For purely thermal convection a linear perturbation analysis shows that a weak thermobaric effect acts as a destabilizing influence on the Rayleigh-B¿nard problem. This is also the case when Earth's rotation is taken into account. In particular, for marginal stability in the absence of rotation, it is shown that two-dimensional convection cells are asymmetric with respect to the midlayer plane, with stronger circulation in the deeper part of the layer. This effect is also revealed by two-dimensional, nonlinear numerical computations, when the layer is stratified by opposing gradients of heat (acting destabilizing) and salt (acting stabilizing). For thermobaric convection, i.e., in cases where the layer would have been stable in the absence of the thermobaric effect, the computed cell pattern is seen to be displaced toward the deeper part of the layer. Furthermore, the cell width increases with increasing thermobaric strength. It is suggested that thermobaric convection may act in conjunction with haline convection due to freezing in the process of vertical mixing and deep water formation in polar areas. ¿ 1997 American Geophysical Union