In order to understand the effects of non-concentric positioning on postglacial rebound in the presence of lateral lithospheric thickness variations, vertical displacements are calculated for disc-like loads placed on non-axisymmetric earth models. Results show that removal of concentric positioning do not produce significant effects that can be resolved by relative sealevel data, and the edge of the ice load remains most sensitive to the effects of lateral heterogeneities. This implies that earlier results of axisymmetric models can be extended to fully 3D laterally heterogeneous models. ¿ 1998 American Geophysical Union