A revised estimate of the spin axis precession rate of Mars has recently been obtained via analysis of range and range-rate data from the Viking and Pathfinder landers. When combined with existing estimates of the degree 2 spherical harmonic coefficients of the gravitational field, this yields a complete determination of the inertia tensor of Mars. Despite this progress, there are still numerous unresolved issues related to the internal structure and rotational dynamics of Mars. We compare results of two different approaches to this problem. In one approach, the observed gravitational field is conceptually partitioned into hydrostatic and nonhydrostatic contributions. In the other approach, the input to the system is partitioned into rotational and load components, and the internal structure (density and elastic rigidity) determines the response. We demonstrate that there is an important, and still unresolved trade-off between lithospheric thickness and the shape of the load component of the gravity field. As the lithospheric thickness is increased, the required load departs more from axial symmetry. The load corresponding to zero lithospheric thickness is nearly symmetric about an equatorial axis, but if the lithospheric thickness is closer to 100 km, the required load is a fully triaxial ellipsoid, with the intermediate moment of inertia halfway between the least and greatest moments. The symmetry of the load has considerable influence on the long-term rotational stability of Mars.